The lenders' SVR isn't technically linked to anything. It's their 'Standard' rate that they can (in theory) set at any level they like. In practice though, it would probably be linked in some way to LIBOR. LIBOR does fluctuate much more than Bankl of England Base Rate, reflecting movements in...
There will be LOTS of people who took out mortgages 3/4 years ago linked to LIBOR. Most sub-prime lenders used to use this rate, rather than the Bank of England Base Rate.
It will be interesting over the coming months.