Agree with what being said below about IB - very good reputation. Some schools do IB for primary years, GCSE (or IGCSE for middle years), and IB again for last couple of years (pre-uni). (Eg, UWC) A friend of mine has son at the The Overseas School (forgotten the proper name - sorry!), and is so happy with IB she is looking for IB when she moves back to UK. Also, re. British Cirriculum, my dd current school is doing IB while following a slightly modified British Cirriculum ... IB is a learning style, principles, ethos, rather than a curriculum.
If you are planning on being in Singapore for many years, over time the "British" angle may become less important as you take up the opportunities offered by the international/asian aspects. (Eg, opportunity to learn mandarin, understand asian geography, history etc). My dd's school study some Chinese history instead of doing Tudors for instance plus Mandarin. Makes perfect sense to me both to help her understand the local culture and the materials are more accessible in museums and in local city for field trips etc.
You may find the waiting list moves quicker than you expect, although the school won't necessarily say that. (Eg, Tanglin, UWC). There are 180 places per year in infants, and although it may not be likely that so many move, over the summer there will be movement and parents tend to have kids on lists for multiple schools. For little ones your kids ages, there will be options (eg Chatsworth, Dover, etc) to start with and you can move them after a few months. It's not ideal, but if you are planning on a longterm assignment, it might be worth the small disruption. Once you get one child into the school, the other will move up the priority list automatically. (Has the priority for British passport holders been removed at Tanglin - that used to help but I do remember they were talking about removing it.)Also, you are more likely to get a place if you are prepared to take a place mid year, or even mid term. Speaking for Tanglin, it's a v. friendly school and kids who moved into my dd's class mid term settled quickly.
Good luck with all the decisions. When we left Singapore I went through similar challenges to get a space at my dd's current school. I even reached the point of thinking I may have to home school for a term which would have been v. difficult for my v. sociable dd and very stressful for my nerves. We were fortunate that she did get a place a month before we arrived.