I think if you really want to see inside a school you can be a bit creative... be near the gates at drop off/pick up times [how happy are the families coming in/going out???] or trawl their websites (most of them will have newsletters or class pages you can look at) or check if any of them are having events which are open to the public (such as an Easter Fair [Fayre?] or similar and go along.
However, I'm with a lot of PPs. I work at more than 1 primary, and am often asked to show perspective parents around. I view it as a MASSIVE pain. You get a LOT of perspective parents if the school's got a decent OFSTED rating or a good reputation locally. It's never as simple as just a tour... they've always got all these questions based on their own thoughts about things. So:
What's your homework policy?
What clubs do you have available?
How do you discipline children?
What trips does the school offer?
What do you do for gifted/talented?
Or unashamedly niche....
What music is there available?
What languages are spoken?
etc.
It's NEVER just an "the answer is X" question. No, cue some long debate from the parent who doesn't think there's enough homework/doesn't think there should be homework/wants a detailed answer on how the homework is marked/has VIEWS on homework they feel they need to share.
Ad infinitum, on whatever the question is they've originally asked (and, sometimes, several of the above)
And I try, I REALLY try to be helpful and friendly and polite and give them the level of detail they want to know ("but what if it's PE outside and it's RAINING????"), but ffs... they're probably going to pick the school with the highest rating by OFSTED anyway (they usually do), and - honestly - I don't care. I'd rather give my time and energy to the parents of the families who actually DO attend the school and, therefore, the ones who these theoretical issues actually DO affect.
And from what you say, you need to pick a school (or 3 schools) and cross everything and hope there's a place. But given that you've already suggested they might go private, then what do the tours matter anyway?
I agree with the PP who said you'd be wiser to look more at secondaries.
And, incidentally, I REALLY admire the secondary schools around here... they'll offer an open day or two in the run up to the admissions process, and they won't talk to ANYONE unless the child is offered a place. Already got sibs at the school? Fine, come back and talk to us after the beginning of March ONCE YOU'VE BEEN OFFERED A PLACE! Until then...