For British curriculum there are 3 options- Kellett (where mine go), Nord Anglia and Harrow. Easiest to get into late in the day is Nord Anglia. It's a new school but I hear a lot of good things about it. However, as far as I know, it doesnt have a reception class (starts in Year 1) so your youngest would need to do another year of pre-school, for which there are many options- they are typically half day programs although some offer extension days.
The other "popular" option is ESF schools which follow the International Bacc. primary years program. They have a different cut off system - Jan 1-Dec 31 so your DC may be in a different year to what they'd be in in the UK, depending on how their birthdays fall. Again, there's no reception and you start Year 1 in the September of the calendar year in which you are 5. The reason I mention ESF is that they save some places for newcomers who don't have school places sorted. This is an endless source of resentment amongst longer term residents but may well work in your favour. ESF schools work on catchment basis so best thing to do is contact them, try to get a place and then live near whichever school is allocated.
As city mentioned, there are also loads of other international schools, and most are not restricted to that nationality, although they probably give priority. Some have international (English medium) streams in addition to their local language streams (French and German Swiss, for example). Some are also selective - if your DC are v bright, this can be an advantage.
Without wanting to offend anyone whose kids are there, I would avoid Canadian at the moment as it's going through a period of major upheaval.
Finally, just as a heads up, HK schools usually go back mid-August rather than early September, as they finish end of June.