By Huw Jones and Christina Fincher

LONDON (Reuters) - Bank of England policymakers said on Tuesday they would press ahead quickly with a new curb on banks' risk exposure based on their leverage, despite industry lobbying against the plan.

Paul Tucker, the central bank's deputy governor for financial stability, told British lawmakers that the new rule should be introduced now.

Some bankers have complained that demands they build up capital levels runs counter to calls from the government and the Bank of England that they lend more in order to boost the country's slow economic recovery.

Andrew Bailey, another BoE deputy governor who is in charge of prudential regulation, also said he wanted the rule in place as soon as possible and that BoE staff were looking at plans submitted by banks for how they could implement it.

"We have made clear that we will go through these with the public, with the institutions during the course of this month. And we will publish. We will make clear what the outcome of that is," Bailey told parliament's Treasury Committee.

Britain's Prudential Regulation Authority (PRA), which Bailey heads, said on June 20 that it would set a leverage ratio of 3 percent for UK banks, which would limit the amount they can lend relative to their capital.

The leverage ratio measures capital against total loans and some bankers argue the new plan would penalize low-risk, high-volume businesses like trade finance and mortgage lending.

The PRA has said that Barclays , one of Britain's biggest banks, has a leverage ratio of 2.5 percent after adjustments, for example.

Some bankers have said they were surprised by the decision to push for the new requirement now, nearly five years ahead of an internationally agreed deadline.

Barclays warned on Friday it may have to cut lending if it is forced to act quickly to meet the new financial target.

Mervyn King, a few days before he stepped down as governor of the Bank of England, last week accused British banks of lobbying senior politicians to undermine the push for more regulation.

Tucker said on Tuesday that lobbying by banks was "unacceptable."

Bailey, also asked by lawmakers about King's comments, said he had been reassured by the government that it considered the PRA to be independent as a bank supervisor.

"We are certainly aware that there are conversations that happened between the banks and officials and ministers," he said. "The thing that concerns me is that we are trying to build, frankly, a transparent process that has accountability in it."

Bailey said there had been "slippage" in the progress of British banks building up their capital buffers.

(Additional reporting by Li-mei Hoang and Adam Jourdan; writing by William Schomberg; Editing by Susan Fenton)