It also disclosed that the joint offer from Pollen Street Capital, its largest shareholder, and BC Partners, announced on Friday, had been an improved offer from an earlier bid that had not been made public.

Analysts at Liberum said they expected the bidders could yet come back with another improved offer.

Shawbrook, founded in 2011 and listed in 2015, specialises in lending mostly to small and medium-sized companies but has been hit as the sector faced declining margins. Its shares have been trading below their IPO price in recent months.

Pollen Street and BC Partners offered to buy the bank for 330 pence per ordinary share in cash and allow shareholders to keep a final dividend of not more than 3 pence per share, Shawbrook said on Friday.

The proposal was 22 percent above Shawbrook's closing share price on Thursday.

"Taking into account the terms of the revised proposal, the confidence the Board has in Shawbrook's strategy and plan and the feedback from Shawbrook's major institutional shareholders, the Board has concluded that it is not willing to recommend the consortium's revised proposal," Shawbrook said in a statement.

Pollen Street and BC Partners said they were surprised by Shawbrook's rejection, adding that the lender had conveyed it was "comfortable" with the improved offer.

The firms also said that after making the offer they had met with Shawbrook's shareholders to discuss it.

Analysts said the offer undervalued Shawbrook.

Liberum said the starting level for a successful bid should be at least 350 pence per share.

"Despite Shawbrook's assertions that it remains confident in its strategy as a public company, we do not rule out a further third improved bid by the consortium," Liberum analyst Portia Patel said in a note.

Shawbrook's shares fell 3.8 percent in early trade on Tuesday, after rallying 19 percent since Friday on news of the bid.

Britain's so-called challenger banks have been increasingly seen as ripe for takeovers in recent months, bankers advising on M&A activity have said, as a prolonged period of low interest rates has squeezed earnings and the pound's fall has made them cheaper for foreign buyers.

Shawbrook also reported on Tuesday a 14.1 percent rise in full-year underlying pretax profit to 91.4 million pounds, which analysts said was in line with expectations.

Loans and advances to customers rose 22 percent last year to 4.05 billion pounds, Shawbrook said.

It disclosed that it had rejected an initial bid from Pollen Street and BC Partners at 307 pence per share in January but had then engaged in talks with the two private equity firms about a revised proposal.

(Reporting by Abhijith Ganapavaram and additional reporting by Noor Zainab Hussain in Bengaluru; Editing by Mark Potter and Susan Fenton)