first things first.

not all part 2 qualification is offered via masters degree. in malaysia and most UK unis offer part 2 as a degree programme. it doesnt matter really in architecture, bcoz all the industry cares about is whether u hold a part 2 or not, not how far u've studied.

but it does concern the students, as the masters, a post-graduate degree, usually costs a few thousands more per year than an undergraduate degree. if money is an issue, u might be better off looking for a part 2 degree programme.

going into ur issues:

if u take degree in taylor's, the requirement for any part 2 universities is primarily a part 1 qualification. remember that taylor's degree is not accredited with part 1. so even if u graduate from there, u still do not hold sufficient qualifications to proceed to part 2.

so without a part 1, there's a possibility u wont get enrolled. however, most universities may consider u, if ur results are good with an exceptional portfolio, to join in at final year part 1 (3rd year 1st degree). finishing off the final year will award u with a proper part 1 qualifications, and later u will be able to continue with their part 2 programme. yes, it does take longer.

optionally, u could attempt to take ur part 1 exam independently. inquire with taylor's as how u can do that.

NUS do accept degrees from private universities, but similar to malaysian IPTAs, they would only consider u to a part 2 programme IF u've fulfilled the part 1 requirements.