I know that some companies do offer flex time, meaning if you come in early, you can leave early, if you come in late, you can leave late, but you still have to work a full day (e.g. 8-4, 10-6). I don't have kids, but others probably know about other arrangements, like working non-school hours. I was once offered a job in the US which involved working in the early morning and evening, so that I'd be home when my kids came home from school--if I had kids.
I would suggest you look for work at a large company, as a smaller firm may not have anyone to cover your position if you are not going to be around at certain times during the day.
I know that here in the states, you can often find flexable hour positions that pay fairly well, and still allow you to not work full time hours.
OK. I reread this and I am confused. Are you looking for flexible full-time work, or part-time work? Do you mean part-time work where you can work whichever hours you want, or not work the same shift every day?
From my personal experience working at a large company in the States, the IT people were the ones most likely to be required to work overtime, on weekends, etc., because if a system goes down on Friday at 5, it has to be up and running by Monday at 8. Although things seem to go at a slower pace in the UK, so that may not be the case here.