if u are looking for new clubs, then don't bother. Prices in Singapore are cheaper
Lilywhites is probably the nearest and biggest store in central london. Apart from clubs, you can check out the clothing, shoes and accessories, some of which are quite cheap / can't be found in Sg
if u are looking for used clubs, best bet is eBay. Just make sure u buy from reputable seller to avoid fakes. A lot of ebay sellers are in fact golf shops located in the outskirts.
The other online alternative for used clubs is golfbidder.co.uk
Finally, if u fancy a round of golf, you can try Trent Park golf course, which is located within walking distance from Oakwood tube station. They have a Nevada Bob's golf pro shop on site, which has a small selection of used clubs, as well as the usual stock of new ones.