Adds name of bill in paragraph 2, Reeves para 4, bank size details para 5, source on legislation details 6

LONDON, May 13 (Reuters) - Britain's government has committed to updating the law underpinning the ring-fencing regime, which requires banks to separate their retail business from riskier activities such as investment banking.

In a document published on Wednesday setting out parliamentary priorities, the government said reforms to the regime, to be included in a new Enhancing Financial Services Bill, would unlock more finance for UK businesses.

“Improved competition in small and medium-sized enterprises' (SME) lending will help small businesses access finance," the government said.

Britain's finance minister Rachel Reeves last year promised "meaningful" reforms to ring-fencing, part of government efforts to slash red tape to boost economic growth.

The rules kick in for banks with more than 35 billion pounds ($46.1 billion) in retail deposits and cover Lloyds [RIC:RIC:LLBP.UL] , NatWest NWG.L , HSBC [RIC:RIC:HSBCUK.UL], Barclays BARC.L and Santander UK SANS_pa.L.

Britain’s finance ministry and the Bank of England did not immediately respond to a request for more detail on the proposal, although a source at a large UK bank said they understood it to mean legislation that would permit essential back-office functions to be shared between the ring-fenced and trading bank - which is prohibited under existing rules.