Im not really sure, but one would consider QE as they have been doing recently. is the BoE the only institution in the UK that can alter the S of money?
In terms of controlling the money supply you should read up on 'Open Market Operations' and other tools used by the BoE to control the money supply. Any basic macro book will have this in. Also make sure that you understand what the 'Monetary Policy Transmission mechanism' is. Also it would also be worthwhile getting to grips with the different measures of the money supply used in the UK (e.g. M1, M2 etc).
In terms of whether monetary policy can actually influence real gdp, it all depends which school of thought you believe. For example, read up on Lucas/Lucas Critique (monetary policy has no real effects in the MR/LR). New Keynesians believe that due to nominal rigidities in the economy (sticky prices/wages and staggered wage contracts) monetary policy can have real effects.