The increase was largely driven by remortgages, reaching an overall 133,116 from 130,643 in October, the data showed.
Remortgages were almost 54,000 of the total – and well above the six-month average of 47,511.
It comes as the Bank of England raised interest rates for the first time in 10 years in November, taking the base rate to 0.5%.
At the same time, net mortgage lending also lifted to £3.5bn, from £3.3bn in the previous month.
Activity staying strong
Jeremy Leaf, north London estate agent and a former RICS residential chairman, said: “There is no sign of collapse in activity, despite the interest rate rise which was happening around this time.
“Of course, some caution must be taken as the gross figures include a large proportion of remortgaging as borrowers sought to protect themselves from further rate increases.”
The mortgage market looks set to remain buoyant in 2018, according to critics.
Mark Harris, chief executive of mortgage broker SPF Private Clients, said: “Already this year a number of lenders such as Barclays have cut the pricing on their fixed-rate mortgages, so there are no signs that mortgages are going to become much more expensive anytime soon.
“Lenders remain keen to lend and competitive deals will continue to boost the number of people remortgaging.
“While the Bank of England figures reflect an uplift in the number of people remortgaging towards the end of last year, the start of a new year is traditionally a good time to look at your finances and consider whether you are paying too much for what is likely to be your biggest monthly outgoing.”