Tokyo is a pretty easy place to live with small children. There are plenty of international pre-schools, though if you feel like being a bit more adventurous, quite a few people use the Japanese nursery/kindergarten system - I did, but I was a long-term, Japanese-speaking expat, which made it easier.
The majority of expats are concentrated on the west side of central Tokyo, mainly because most of the international schools are around there. The British school has two campuses - one not far from Shibuya station, and one a little further west from there, so British families are most likely to be found in that general area, ie in Minato-ku, Shibuya-ku, Meguro-ku etc. And international preschools have also popped up all over that side of Tokyo.
Housing, if you have a generous package, can be pretty good. Either large apartments if you are somewhere more central - some of them have shared facilities like swimming pools - or houses if you are a little further out. Don't expect a garden though - you might get a terrace and a small ornamental garden. Rents are not as bad as they used to be, eg Hong Kong is more expensive these days. I don't know how it compares to Singapore.
There are growing numbers of expat couples where both partners work, but SAHMs are still much more usual (hard to find a job as a trailing spouse unless you have very portable skills or can set up a business; childcare can also be tricky), so there are plenty of mother and baby groups and classes etc going on. If you don't mind being in a totally expat environment, and the company will pay the fees, the Tokyo American Club has swimming pools and lots of activities.
It's definitely worth going for a look around, and maybe asking one of the international estate agents to show you round some typical areas and properties. Does your DH's company have someone in the local office who would be in charge of relocation?
Useful online resources are Being a Broad - magazine/website for foreign women in Japan (discussion board here; Foreign Executive Women - networking group for foreign women ('executive' is a bit of a catch-all title - it's really for any working women); Tokyo Families magazine.