Free gym/swimming/badminton etc. may sound like a luxury but the BeActive scheme run by Birmingham's NHS and the City Council has been a tremendous success offering exactly that.
Hard to reach groups getting involved and all groups (ages, income etc.) are taking part in physical activity more often and of course the benefits of this will, in the long-run, pay for itself in savings to the NHS.
The BeActive scheme also shows how you can move beyond simply offering free access to facilities to actually create a membership community. Getting residents to sign up and get a members card allows Councils or new English City Regional Mayors' offices to gain data on how often facilities are being used and also a way of contacting individuals to target them with tailored promotional material about the facilities or the activities on offer.
Savings in the future might sound all well and good but leisure centres could do with some revenue here and now so why not use the membership scheme to its full advantage by working with a list of organisations (shops, experience day providers, restaurants etc.) to offer money off in exchange for points accrued (ala Nectar cards) for attending leisure activities. This has the twin benefit of providing advertising for these businesses who could pay to sign up and it also encourages citizens to stay active and use the facilities often in order to gain points.
So how about it? A policy that extends the entitlements provided in exchange for the hated Council Tax, a policy that gets the population more active and saves the NHS money/makes workers more productive at the same time; and a policy that brings in revenue from the private sector whilst saving individuals money in shops and restaurants simply as a reward for being healthy and active.