BM Solutions, subsidiary of Lloyds Banking Group, and The Mortgage Works, a subsidiary of Nationwide, together account for between 67% and 89% of the market share of buy-to-let mortgages.
Nigel Stockton said: “One of the things we talk about is all these new lenders coming into buy-to-let but let’s not be under any illusions, we’ve got two dominant lenders in BM and TMW.
“If either of them for any reason at all step back from this market, it would be catastrophic.
“We say that it’s a very competitive market place but it’s not really. If BM said they would close shop for a little bit and they were going to put £4bn into first-time buyers, which Lloyds are perfectly entitled to do, then the market is a bit snookered.
“So we actually need big lenders like Royal Bank of Scotland and Santander to come and play properly, provide proper competition and actually see where margins do settle down and reflect risk more accurately.
“Whilst we’re talking about the market doing well, it is but so long as TMW remains committed and BM remains committed.”
A Santander spokeswoman said: “Santander constantly reviews all areas of the market and one area we are taking a close look at is the buy-to-let market, specifically the non-professional landlord sector.”