I understand that Belgium is an excellent place to buy diamonds & gems (they are traded there) so you could have a stop-over in Brussels (which is apparently lovely) next time you go to the UK. Or you could go to Hatton Garden in London or the Jewellery Quarter in Birmingham city centre. You can choose a gemstone and design your own setting and style of ring. The gold or platinum of course would be hallmarked, I'm not sure if it is in Singapore but is probably is. And of course if you buy in the EEC you can reclaim the VAT back when you leave! Make sure you get a written guarantee and also take out insurance for the ring.
Another idea is to buy something in Dubai as gold there is weighed on scales and charged accordingly - so is apparently very good value for money. Perhaps you could check with the Emirates airline (v.good and Dubai is a good stop-over en-route to the UK)if they or the UAE Embassy can give you any info about where to find reputable places.
Congratulations!
I think I would avoid the gold in Little India as it is very yellow compared to the gold as most Westerners are used to.