The availability of mortgages increased further in the first three months of this year, and the rise was slightly more marked for low-deposit borrowers with loans-to-value (LTVs) of 75% or more, the Bank's credit conditions survey found.
Lenders reported that mortgage deals became significantly cheaper for borrowers in the first quarter of this year, as they passed through cheaper funding costs to borrowers and ramped up competition.
They expect mortgage rates to be slashed further over the next three months, as demand increases for both prime lending and buy-to-let lending.
The Government's Funding for Lending scheme, which was launched last August and gives lenders access to cheap finance, was cited by many lenders as a factor pushing down on bank funding costs and helping to drive down lending rates.
Previous research has found that the number of mortgages on the market has already increased by around one third since the scheme began.
Despite the increase in mortgage availability and the drop in rates, lenders also said their credit scoring criteria was little changed and the proportion of applications which were approved fell slightly.
Analysts said the Bank's latest findings will also pile the pressure on Government to come up with further measures to boost lending to businesses. The report found that an increase in the availability of loans to businesses seen in the first quarter of this year was confined to larger firms, with small and medium-sized companies seeing little change.
Howard Archer, chief UK and European economist for IHS Global Insight, said: "The survey adds to the pressure on the Bank of England and the Government to come up with further measures aimed at boosting bank lending to businesses, with the focus particularly on easing credit conditions for smaller companies. A strong possibility is that the Funding for Lending scheme will be adjusted to specifically favour banks that increase their lending to smaller companies."