LONDON (Reuters) - British house prices rose more slowly in September than in August, according to figures from mortgage lender Nationwide, adding to signs of a cooling in the housing market after voters decided in June to leave the European Union.

Prices rose by 5.3 percent in September compared with the same month last year, slower than August's increase of 5.6 percent, Nationwide said.

The September figure matched expectations from economists polled by Reuters.

In monthly terms, house prices rose by 0.3 percent, also slowing from a rise of 0.6 percent in August.

Nationwide economist Robert Gardner said the modest slowing of growth in house prices was probably due to a shortage of homes for sale which cushioned the impact of weaker demand.

"The relative stability in the rate of house price growth suggests that the softening in housing demand evident in recent months has been broadly matched on the supply side of the market," he said in a statement.

Britain's housing market has shown other signs of slowing since the referendum, although the introduction in April of a higher tax on landlords buying properties has also weighed on the market.

The Bank of England said on Thursday that the number of mortgage approvals in September were the lowest since late 2014.

However, consumer confidence remains largely intact after the Brexit vote. Market research firm GfK said on Friday that its gauge of consumer confidence jumped in September back to the level seen before the referendum.

(Writing by William Schomberg; Editing by Louise Ireland)