Thanks for the replies. I realise I'm taking a risk by coming over first but I figure it might be the best way to find out what jobs are available.
To Vaucluse: I have a UK passport so that should give me 30 days to find work, possibly longer if I can get an extension. When I mentioned buying a one-way ticket I didn't realise that this might be a problem with Immigration so I guess I will get a return flight instead.
As for the kind of job I'm after, well anything really. My background is in New Media (Web Development), but it's very specialised and I have a strong feeling that I will be underskilled for the New Media industry in Singapore. So whilst I will be concentrating my efforts in that area, I'll also be happy to look for office admin jobs, point-of-sale etc.
I'm under no illusions that this is going to be easy, but I'm prepared to explore all my options before I give up on this idea.
Anyway, thanks again. I'm going to ring up a few agencies tonight - at 3am UK time

- and will let you know what they say.