My favourite place is just off the lobby area at the "Regent Hotel". Very English... lots of lovely sandwiches, petit fours, variety of cakes, scones, tea-breads etc. Lashings of tea (Earl Grey, Darjeeling etc.) or coffee. And a pianist too. They start early too - about 1.30pm until about 5.30pm or 6.00pm. Nice and leisurely. If you're driving there, give them your parking coupon and they will annotate it for complimentary parking. Enjoy!
(I know what you mean about the other places - I found Raffles very disappointing, and the Shangri-La and Goodwood Park don't cut it either. But do try the Regent, I'm sure you'll like it).