Why would you pay such stupid fees?

?? we are Brits and lived here going on 20 years without setting foot in the British Club. You can have a great social life without paying joining fees, not to mention your monthly fees....
So if you had bitten the bullet all it costs net is the transfer fee (about 3k-4k which is hardly stupid), so about 50c per day for your time here. Even if you were only here 2 years 5 SGD a day is not much different to what a lot of people spend on a gym alone.
Clubs have gyms, pools, squash, tennis plus bar and restaurants and other activities, increasingly things like onsite spas. Some condos cover much of this but not all and quality is generally lower. F&B is generally a lot cheaper than outside as well.
Generally there are monthly minimum spends, they are low anyway if you ever actually go.
Some clubs do have stupid fees (e.g. SICC) British Club isn't one of them and not everyone lives in a condo with good facilities. Costs actually work out pretty cheap in the long run, you may wish to open your mind a little.