"We suspect the effective floor on rates will be 0-0.25%, with an initial cut in the Bank Rate to 0.25% coming over the next couple of months."
Ian Kernohan, Economist at Royal London Asset Management, said it is likely that the Bank will wait for the full set of July survey data to be available in August.
Kernohan said: "The magnitude of interest rate reduction is a moot point, since if rates are cut too far, there will be a knock-on impact on bank profitability, which would result in policy tightening. We suspect the effective floor on rates will be 0-0.25%, with an initial cut in the Bank Rate to 0.25% coming over the next couple of months.
"It will take some weeks to assess any Brexit impact on the UK economy. Last week’s manufacturing Purchasing Manager's Index survey was a little stronger, although it was taken before the result of the referendum was known. Mark Carney has said that the Monetary Policy Committee will give an "initial assessment" of the economic situation at its July meeting, and then discuss the situation further in the run-up to its August Inflation Report."
Last week, Mark Carney has said that in his view "the economic outlook has deteriorated and some monetary policy easing will likely be required over the summer".
Immediately after the Referendum result, the swaps market gave a 50% chance of an interest rate cut in July, a 65% chance of a cut by August, and an 80% chance of a cut by the end of the year.