There are several clubs that do sell a day pass but I don't know any that have showers, except for the AA Arrivals lounge in T3 (landside) which will let you in for a small fee (something like GBP 30). Very nice showers, almost as good as in the BA Arrivals lounge in T4 (which doesn't let you in flying WTP). Obviously the public showers are considerably cheaper (circa GBP 3 or 10% of the cost).