I love the afternoon tea at The Regent hotel.......lots of cakes, petit fours, scones with jam and cream and desserts

It's a nicer ambience than The Goodwood Park. They bring all the food to you at the table. I'm sure if you explained that there is a veggie (maybe when you book) they will offer a nice selection of veggie savoury sandwiches.
My mum did not enjoy the one at Raffles at all (she was hoping for a traditional afternoon tea but it had more local savoury food than she anticipated....).
Another place worth checking out is at Equinox at the top of the Swissotel (the Stamford) as the views are wonderful, but you have to keep getting up to get the food, rather like a buffet.
I can't post links but there was a great review of "High Tea in Singapore" in the UK Daily Telegraph in April 2010....do a search online.