Cunliffe (pictured) told BBC Radio 5 Live if house prices continued to rise faster than incomes the housing market would become a cause for concern.
Bank governor Mark Carney moved last week to cool down the housing market by introducing new restrictions on lenders.
Banks and building societies will only be able to lend more than 4.5 times a customer’s income to 15% of their portfolio.
“Some months ago I thought the biggest risk at that point came from the UK housing market in Britain,” Cunliffe said.
“And it’s not the risk around house prices as such, it’s the risk that we get a sustained rise in house prices – and this is very important – (the risk of) house prices rising faster than people’s incomes.
“That leads to the sustained increase, a big increase in the amount of debt in the economy, in the amount of debt that mortgage holders have.”