Caporegime
The LIBOR rate hasn't changed, the Bank of England has lost all control of Interest Rates, they could drop it to 2% but if banks don't follow then it's meaningless.
LIBOR rate only affects fixed rate mortgages, which if you already have one obviously isn't going to change, so it's only people trying to get a new fixed rate mortgage who aren't affected by the interest rate cut. People on most tracker, flexible and SVR mortgages (over 40% of the market I believe) have had the rate cut passed on straight away.