What are the state primaries like in your area? Not all private schools are the same, the teaching in them is not necessarily better than that offered in local state schools.
If your local state primaries are 'good' or better (using the full range of information at your disposal, e.g. OfSTED reports, visits made as prospective parents, information from other parents etc.), you may find that you'd be happy educating your kids in the state system. You could pick up any shortfall in sporting or cultural activities with paid for after school clubs/weekend activities 'en famille' (e.g. trips to museums etc.) and the extra contact time you would have with them (as you'd be able to reduce your hours of paid employment).
If your local state schools are dreadful, would a move be possible? Or would you consider Home Educating?
The other thing that occurs to me is, whilst you have greater influence over the 'moral education' of your children (once they reach their early teens, their friends and media will play a larger part in this), you can still have an impact on the people they grow into. Personally I'd invest the money in private education at secondary level if the local state schools weren't any good (or put the money aside to fund a move to a place with better state schools) - they could then do their secondary stint somewhere where the ethos was more aspirational, classes were smaller, access to wider range of extra curricular activities etc.
If you considered that route, you'd have the primary years to work part time and save for the secondary years - so you'd get more time with your kids but still invest in their education at more of a crunch point.
Just throwing these into the mix for your consideration.
However, WRT to the question of whether you are BU to work FT or not, as others have said, that is totally your call. Some may have very strong opinions one way or the other, but until we can walk in each other's shoes, it's impossible for one parent to comment on another's work/life balance.