In Summary, I did, I wouldn't again.
Once they're in the system it's very difficulty to move them out again, away from their friends and into an environment where they'll be treated as lepers, snobs, rich bastards and so on. So the later you begin spending on private education, the better, because IME there is no going back.
Now to the education. A bright, well motivated and parentally well supported child will do just as well in a good state comp as they will in a private school. In fact my local comp regularly turns out students who achieve 3 A's at A-Level. Of course, the private school does that too, and as a percentage generates many more students who achieve that. But it costs a lot of money to achieve that (min. 7 years at £10k p.a.). Of course it's not just about results. They will get more opportunities at a private school with a wider variety of sports and activities that a state school has neither time nor money to accommodate.
The social aspect. My kids would have been better off at the local school with local friends within walking distance, rather than at a school 15 miles away where the pupils come from a wide area. My (now late teens) kids are a little lost in their own home town because they don't know anyone.
The cost. Your daughter is two I think you said. You have to consider what if the marriage goes wrong, you'll have a daughter at an expensive school that neither of you can afford to pay for (I'm assuming you'll end up much worse off after a divorce, this is my experience and that of many others I know). Of course, you won't want to traumatise your kid any more so you'll do your best to keep her at the school she knows. This will kill you financially and may even then result in you having to change her school eventually anyway, back to the local comp. I advise this: if you can save now and pay for the education from savings later on, then go for it. But if you'll be relying on your continuing income to pay for it, you can't afford private education, so don't do it. Think of it like Capex vs. Opex.
I think it was Churchy who said something like, why not keep her in state education now, start saving, and think again when she's approaching 11 years of age. I think that's very good advice indeed.
You'll have to be able to defend your position from your missus who's clearly keen on the private option. Good luck with that. But believe me, it's worth it.
If your local state schools are that bad, just move house.