It will also accept business from firms which are already on its approved panel for undertaking business lending work.
The new arrangements for England and Wales will apply to all applications received on or after April 16 2012.
Arrangements in Scotland are unchanged.
Desmond Hudson, chief executive of The Law Society, says: “Lenders make their own decisions about their panels, so we regard Clydesdale and Yorkshire Banks’ decision to make CQS a requirement for panel membership as further demonstration that CQS is a trusted community of skilled practitioners.
“Not only is it an assurance of high standards in conveyancing for lenders, but by showing its commitment to CQS, they are also putting customers’ interests first by maintaining a wide panel of trusted firms.”
The Law Society has so far accredited 1,300 firms in England and Wales.
The news follows HSBC’s decision to restrict its conveyancing panel to 42 firms, earlier this year.
Speaking on the BBC’s Radio Four Money Box programme at the weekend, Martijn Van der Heijden, head of lending at HSBC, defended the bank’s decision.
He told the show’s host Paul Lewis that it made the changes to reflect what is happening in the lending market, with other lenders restricting their panels to combat fraud and for regulatory reasons.
Hudson responded by calling the changes badly thought out, disorganised and unnecessary and suggested if the bank was worried about the quality of the firms it used, it should only use those accredited by The Law Society.
However, Van Der Heijden told Hudson: “Our data shows that over 99% of our cases since we restricted the panel have gone through without a hitch.”