After doing some in-depth research to find the original research or reports I've found nothing published by the Hungarian institutions nor Dr Jesse Bloom - the only person quoted in the article. Having dug further I don't take his statements at face value either, for the reasons described below, since there's more than a hint of preconceived bias in his general thrust and previous publications.
I REALLY wish journalists would clearly share published sources to original research and data for such important events rather than stir up controversy without demonstrating a strong foundation. Especially when claiming this is a "finding".
For clarity, I've no opinion on SARS-Cov-2 origin but I do want to see claims well-supported by evidence.
I went looking on both the mentioned Hungarian web-sites [0][1], searched biorxiv, and checked the Bloom Lab [2] publications since the only person quoted is Jesse Bloom [3] who claims to have reproduced (Hungarian) results. In my research I also found a prior report by Bloom in June 2021 [4] reporting 'recovery of deleted files containing partial sequences' [4] that were soon criticised by multiple other scientists; e.g: "...The language of the paper is unusual, its contains a significant degree of supposition and conjecture, cites blog posts..." [5].
[0] https://univet.hu/en/research/topics/
[1] https://www.elte.hu/en/facts
[2] https://research.fredhutch.org/bloom/en/publications.html
[3] https://research.fredhutch.org/bloom/en/members.html
[4] https://www.biorxiv.org/content/10.1101/2021.06.18.449051v1....
[5] https://edition.cnn.com/2021/06/23/health/coronavirus-sequen...
Updated: just discovered there's a recent github repo [6] created by Bloom with much more detail. Telegraph should really have pointed to this.
[6] https://github.com/jbloom/PRJNA692319_public
Update 2: Pre-print [7] of the Hungarian report (see [6] for details as to why it was rejected by Biorxiv several times).