The Office of Fair Trading said it has received confirmation from 48 out of 50 lenders that they intend to prove to the regulator that they are acting within the rules.
It comes as a charity has warned that "out of control" lenders are failing to act responsibly. An OFT spokesman said:
Of the 50 payday lenders that were inspected during the compliance review, 48 have confirmed that they will provide the OFT with proof that they are fully compliant, while two have surrendered their licences.
The OFT has also announced that it has formal investigations open into the practices of three payday lenders and, in addition, three payday lenders have also had their licences revoked since the review of the sector in March.
More top news
Mr Blavatnik, whose empire includes the Warner Music Group, has an estimated fortune of £13.17bn according to the Sunday Times Rich List.
Find out what to expect from the weather if you are running in the big race in London or watching from the sidelines.
It will be a soggy start to the weekend and temperatures will drop making it feel colder than in recent days.