Just came across this today and since I haven't seen it publicised much at all I thought other locals might be interested in knowing.
Prices at Lewisham's leisure centres are due to rise on 1 April by 9% but if you have a valid Lewisham library card you can use the Fusion leisure centres at the old rates for a whole year!
Full details are here - the main points are that your library card must be activated and working by 31 March in order to take advantage, and you must take it with you when you go to the leisure centre.
For some reason it only applies to the facilities managed by Fusion, so if Downham is your local leisure centre it seems you'll be expected to suck up the price rise.
Of course there's a rather sad irony about the fact that with all the library closures in Lewisham you'll probably get more use out of your library card for physical fitness than you will for mental stimulation.