If you have no money it's more advisable to study in a Singapore university and then go for student exchange and/or internship in the UK in your 2nd or 3rd year.
When you go for student exchange, you'll be paying tuition fee to your Singapore university. Financially it's better and more worthwhile to go to UK as an exchange student rather than a full-time UK student... If you manage to get an internship in the UK, it's even better... You'll be paid during your stay in the UK.
4 years ago I also had the same dilemma as you. I wanted to go overseas for my undergraduate studies (I even applied for 6 UK universities and got the acceptance letters), but my family has no money. In the end I studied in NUS. During the past 4 years in NUS, I went to Germany for a summer immersion, Canada for a 6-month internship, Japan for a scientific symposium, etc... and all the trips were fully sponsored. Now, I just graduated from NUS, and I never regretted entering NUS... At least I managed to see the world without spending too much. (I'm the type who like to travel everywhere. Haha.)
Studying overseas is a good thing. But after staying overseas for a long time, you may get home sick and lonely. In addition, you may feel an increasing financial burden... Do you have any experiences living overseas for a long period? If you have no such experiences, spending 3 years in UK may be a difficult challenge. In that case, it'll be better to enter a Singapore uni and do your student exchange or internship in UK. At least a 6-month or 12-month stay will give you less psychological and financial stress than a full 3-year stay. If you love the overseas experience after doing a student exchange or internship (and prove that you can handle your home-sick-ness & your finance), you can always do your graduate studies overseas.
That's my one cent's worth of advice...
