(Refer last para in bold for short answer)
It has been "presumed" by many indolgists (cited many times on the site) that Puranas underwent adulterations over generations. Yet, assuming the statements to be accurate, it can be seen that the content and basic character of the Puranas as being spiritual in nature did not change till the colonial era. For example, R. A. Sastry in the Preface to the Second Edition of the Lalita Sahasranama with Bhaskararaya's Commentary, while citing the Brahma Gita Vyakhya of the Suta Samhita by Vidyaranya on the Aitareya Upanishad says:
It will be seen from the Puranic Manuscripts of the tenth to thirteenth centuries which are very rare to secure that the Puranas were intended to explain the Vedic doctrines to lay minds. But like every other subject, they have degenerated to such an extent that they have lost their real significance and have come to be treated as some childish story. In these days both the reader and the hearer of the Puranas are generally uncultured. The former especially has no spirituality in him... With the revival of our spirituality, I hope the Puranas will regain their original place.
As discussed here, the Skanda Purana published in 1910 (and other Puranas) based on a random collation of manuscripts is different from the Skanda Purana relied upon by traditional acharyas. A similar view has been stated in by Dominic Goodall in the 'Parākhyatantram', Vol 98, Page xvii:
Schomerus’ ... Skandapurana, of which Bendall had found a manuscript in Nepal that he supposed to have been written in the sixth century. From the work of Adriaensen, Barker and Isaacson (1994 and 1998) we know that early Nepalese witnesses transmit a text that is entirely different from what has hitherto been printed as the Skandapurana.
This shows us that the Puranas in vogue during the colonial era suffered from severe adulterations as compared to the manuscripts of the preceding centuries. Now the question arises that if the colonial era and immediate pre-colonial era manuscripts are not original, then who adulterated them?
Ludo Rocher in 'the Puranas', describes that like the Vedic tradition, the Puranas too had a tradition, but the attitude towards their preservation was casual. For example he states that the Agni Purana as quoted by various other texts is starkly different from the extant one, obviously being forged. Rocher described two types of forgeries. One being the innocent kind and the other being the devious kind.
- The Innocent Kind:-
Rocher provides one incident of an innocent completion of a text called Nilamata Purana (not among the 18 Mahapuranas and Upapuranas) owing to the initial part being unreadable:
Another well known case of "forgery" in the puranic textual tradition is connected with the Nilamata0. In 1877 Biihler reported as follows:
"In that case the Maharaja of Kasmir was the innocent cause of the forgery. He ordered Pandit Sahebram to prepare a trustworthy copy of the Nilamata for edition. As the Pandit found that all the MSS. were defective in the beginning, and as he knew from the fragments, as well as from the Rajatarangini, what the lost portions did contain, he restored the whole work according to his best ability.
Here we can see due to a portion being damaged, a Pundit reconstructed the text to the best of his ability based on what he knew about the contents. Here he is not changing the text but merely reconstructing it. As such some wordings may be different, but not the contents of the text. As I stated above, the same is the case with old manuscripts which may or may not have changed the words, but the overall contents and deep spiritual meaning are intact in pre-colonial manuscripts. At the maximum some sectarian acharyas may have changed texts for their God, but not to squeeze out the very essence and spirituality of the text. Thus the adulterations which the indologists so vehemently talk about seem to just be mere word changes.
- The Devious Kind:-
This is the kind that the colonists used to deface scriptures and defame the Pundits for it. Rocher describes an incident of a European named Captain Francis Wilford bribing a Pundit to mar texts in order to prove that the Hindu religion had its origin in the British Isles (according to the European, called Sweta Dvipa). However, he has represented the story trying to show the Pundit in bad light. Quoting the incident:
Captain Francis Wilford, who set out to prove "that the Hindu religion had its origin in the British Isles, which constitute, in his opinion, the Sweta Dwipa, or white island, of the Indian mythologists." Wilford's experience is worth quoting, for it clearly illustrates
the nature of the puranic tectual tradition.
"I consequently directed my pandit to make extracts from all the Puranas and other books relative to my inquiries, and to arrange them under proper heads. ... I have since learned that, as the money for his establishment passed through his hands... perform the task alone, which was impracticable. In order to avoid the trouble of consulting books, he conceived the idea of framing legends from what he recollected from the Puranas, and from what he picked up in conversation with me. As he was exceedingly well read in the Puranas, and other similar books ... it was an easy task for him; and he studied to introduce as much truth as he could, to obviate the danger of immediate detection.
His forgeries were of three kinds; in the first, there was only a word or two altered. In the second, were such legends, as had undergone a more material alteration; and in the third, all those which he had written from memory ... he began to adulterate and disfigure his own manuscript, mine, and the manuscripts of the College [at Benares], by erasing the original name of
the country, and putting that of Egypt or of Swetam in its place... he had the patience to write two voluminous sections, supposed to belong, one to the Scandapurana, and the other to the Brahmanda, in which he connected all the legends together, in the usual style of the Puranas. These two sections, as he wrote them, consist of no less than 12,000 slocas or lines, the title of which he borrowed. The real sections, are so very scarce, that they are generally supposed to be lost and probably are so; unless they are found in the library of the Rajah of Jayanagar.
From the above we can see how after receiving bribe from the colonist, the Pundit changed the name of countries to Sveta and also wrote whole new sections comprising no less than 12,000 verses! Though the colonist orchestrated this incident, yet in his book, he has referred to the Pundit as having evil disposition. We can also see that the Pundit was learned in the correct scriptures but those seem to have been lost.
Since the question quoted Wikipedia, I too would like to finish by quoting Wikipedia on Puranas, before it's removed from there:
Newly discovered Puranas manuscripts from the medieval centuries have attracted scholarly attention and the conclusion that the Puranic literature has gone through slow redaction and text corruption over time, as well as sudden deletion of numerous chapters and its replacement with new content to an extent that the currently circulating Puranas are entirely different from those that existed before 11th century, or 16th century. Many of the extant manuscripts were written on palm leaf or copied during the British India colonial era, some in the 19th century. The scholarship on various Puranas, has suffered from frequent forgeries, states Ludo Rocher, where liberties in the transmission of Puranas were normal and those who copied older manuscripts replaced words or added new content to fit the theory that the colonial scholars were keen on publishing.
If we analyse the Puranic texts in print we will see that actually they are based on the colonial and immediate pre-colonial era Manuscripts and all the above authors are correct. The colonists got stories changed through Brahmins, to their advantage. one such being the misdemeanour of Brahmaji used by missionaries in Andhra to ridicule innocent Hindus (as per Matsya Purana and overlapping Shiva Purana verses. Whereas actually, there was no such incident. Please note: Satapatha Brahmana discusses Daksha Yajna instead of Brahmaji and Brahmaji's fifth head was cut due to harmful Rajas).
So back to your question, " Who were these people who edited the Puranas?" The convenient yet truthful answer given by indologists is - the Brahmins of India. However, in reality yes, the Brahmins did adulterate texts, but at the behest and on being bribed by the mlecchas. So ideally the question should be - "Who got the Puranas changed?" and there you'll have the accurate answer as - the mlecchas with a mission.
You can also refer to another colonial mishap here, where in the 19th century the Vayu and Brahmanda Puranas were confused, whereas the Vayu Purana is merely a synonym for the Shiva Purana. I had also read one other article of list of kings right from Yudhishthira till the Islamic invasion, where the author writes that had this work come in the hands of the British they would have destroyed it