Clydesdale Bank is moving closer towards a merger with Richard Branson-backed Virgin Money, after it raised a bid to form the United Kingdom's biggest "challenger" bank.

Former National Australia Bank-owned Clydesdale, which last month approached Virgin about a tie-up, on Monday released a statement to investors that set out improved offer terms, and said the two sides were in discussions about the all-scrip merger.

Under the revised terms, Clydesdale (known as CYBG) has nudged up its valuation on Virgin, so that Virgin shareholders would own 38 per cent of the combined group, up from 36.5 per cent previously.

It also said the two sides were in "discussions," and that they believed teaming up would create "the UK"s first trust national banking competitor," in the retail and small business markets.

"The proposed combination would provide a powerful full-service banking offer for around 6 million personal and business customers, bringing together the complementary strengths of CYBG and Virgin Money," the statement said.