March 9 (Reuters) - Investment bank Jefferies said on Monday it expects a less than $20 million hit to its earnings from exposure to the collapsed UK mortgage provider Market Financial Solutions.

The collapse of the little-known MFS last month renewed concerns about wider losses among banks and stoked fears of more "cockroaches" in the booming private credit industry.

Jefferies said one of its European subsidiaries had loaned MFS 103 million pounds ($137.42 million) under a warehouse facility secured by certain of the mortgage provider's bridge loans.

Separately, the investment bank said Western Alliance did not extend credit to Jefferies. Western filed a lawsuit against the firm on Friday for not completing a payment of $126.4 million it owed to the regional lender for loans tied to bankrupt auto parts supplier First Brands Group.

"Jefferies has no obligation to pay off a non-recourse loan Western Alliance chose to make to a special purpose vehicle against First Brands receivables. The statement that Jefferies 'couldn't' repay $126 million is false and absurd," the company said.

($1 = 0.7495 pounds)

(Reporting by Arasu Kannagi Basil and Pritam Biswas in Bengaluru; Editing by Sriraj Kalluvila and Maju Samuel)