What seems incredible but is true, the UK Bank of England base rate has been at 0.5% since March 2009.

http://www.bankofengland.co.uk/

What is even more amazing is that anyone is the UK who took out a mortgage since 2007 has never seen a rise in the Bank of England’s base rate.

So an interest rate rise would mean higher payments on mortgages and less disposable spend in the wider economy.
But always be cautious on high level statements.

In the UK there are just under 14.5 million owner-occupied households. However, there are actually 7.5 million people, who have no mortgage at all. So an interest rate rise would be irrelevant, and if they have savings they are actually better off.

Thus there are 7 million people who have mortgages, and they are the ones would suffer if rates were to rise.