Interest rates are increasing, whether the MPC likes it or not. Since the end of January this year, the 12-month LIBOR sterling interest rates has increased 128 basis points. On June 12, the last day the BoE posted data on their website, 12 month sterling LIBOR stood at 6.42.
Inflationary expectatations are taking control of interest rates. The MPC may control overnight rates, but the market determines long term rates. At the moment, the market sees only one thing on the horizon; higher inflation.