This was less than in September and below the average for the previous six months of £3.9bn.
"Comparison of current lending levels with last year is obscured by the very different economic conditions that exist now, reflecting a much reduced appetite for borrowing," said David Dooks, BBA statistics director.
"Mortgage approvals remained low, consumer credit was subdued and people used their deposits to fund spending in October."
The Crosby report was one of the most striking entries in Monday's pre-Budget report in warning about the state of the economy.
It said that banks could be drawing in more in repayments than giving out in new mortgages in 2009.
BBC FOCUS ON FALKIRK
Speaking to local solicitors who have been in Falkirk for 20 years and they have never seen a market as challenging as this present one
Sir James was commissioned by the Treasury to look at ways of reviving the mortgage market.
He is calling for a temporary guarantee with taxpayers' money of new mortgage-backed securities - the bundles of home loans sold on by banks to investors to fund fresh lending.
Without such intervention net new mortgage lending - gross new home loans minus repayments and redemptions - would fall below zero in 2009 and see only a modest recovery in 2010, he said.
In 2007, net new mortgage lending stood at £108bn. This year it is forecast to be £40bn.
Chancellor Alistair Darling said he would draw up a plan based on the proposals in time for the main Budget, but he would require European permission to implement it.
"I share Sir James's concerns about the availability of mortgage finance," said Mr Darling in the pre-Budget report speech.
But faced with such a serious short-term warning, some experts have called on the chancellor to take swifter action.
Ray Boulger, of mortgage brokers John Charcol, said Mr Darling had "completely failed to recognise the urgency" of the main Crosby recommendation.
"The mortgage market needs access to additional finance now."
And buy-to-let firm Paragon, reporting tumbling annual pre-tax profits on Tuesday, also called for swift action to kick-start mortgage lending.
Tuesday's figures from the BBA will feed into industry-wide lending statistics to be published in a week's time.
The BBA said that the number of home loans approved for house purchases was down from 23,383 in September to 21,584 in October.
Falling house prices and the insistence on banks demanding larger deposits were revealed in the BBA figures. These showed that the average value of a new home loan was £153,500 a year ago but fell to £128,400 last month.
"These conditions highlight the difficulties facing first-time buyers, particularly where stringent deposit requirements continue to be a major barrier to those wishing to enter the market," said Oliver Gilmartin, senior economist at the Royal Institution of Chartered Surveyors (Rics).
"Aggressive interest rate cuts by the Bank of England in recent months and the prospect of more to come before Christmas will take time to filter through into increased house sales."
Approvals for remortgaging was up 1% on the previous month, but still down 6.4% compared with a year ago, the BBA said.
The figures suggest that people are drawing on other forms of borrowing.
The amount borrowed on overdrafts from the major banks dropped slightly and demand for personal loans was "weak", the BBA said. However, borrowing on credit cards was in line with recent monthly averages.
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