Experts also fear the base could tumble further to zero, or even into a negative reading, in the coming months.
However cutting borrowing costs could shore up activity in a jittery housing market by lowering mortgage costs.
It will also boost business confidence and companies’ willingness to keep investing.
The Bank’s chief economist, Andy Haldane, has called for a big package of measures to support the UK’s post-referendum economy.
The Bank committee’s policymaker Martin Weale, who has previously voted for rate rises, suggested that he was likely to use this week’s meeting to support some form of stimulus for the economy.