At the same time, the average interest rate for new mortgages dropped for the first time since November 2021, falling by 0.06 percentage points to 5.28%.
However, a fall of £830m in net mortgage lending was also recorded, far below the £250m rise expected by economists polled by Reuters.
House-buying activity had been depressed as mortgages grew more expensive following 14 consecutive interest rate hikes by the Bank.
The continuous Bank rate rises brought the rate to 5.25% in August, a high not seen since 2008 and a position that has been held in subsequent interest rate decisions by the regulator.
Tuesday’s data also showed a growth in the number of people remortgaging – up to 30,800 in December from 25,700 in November.
The trend of increased approvals may be likely to continue as the average mortgage rate on offer for a five-year fixed deal has dropped to 5.18% and 5.56% for the typical two-year fixed product, according to financial information company Moneyfacts.
Latest inflation and growth forecasts will be published by the Bank’s rate-setting committee on Thursday along with its outlook for future rate decisions.