In case anyone's interested, this is what I found out:
Here in Brent you get £416 per 11-week term. You get it pro-rata, so if your child is only doing 3 sessions, then they get 3/5 of £416. The council defines a session as 2 1/2 hours, but ds's nursery does 3 hour sessions - it makes no difference, as it's the number of sessions that counts, not the number of hours.
The nursery applies for it and gets it in a lump-sum, which it is then up to the nursery to decide how it is passed to you (one term we had a discount every week, one term we had the first few weeks free then paid in full for the rest of the term). Outside termtime you pay the full amount - unless the nursery has decided to spread the discount further. The entire amount that the council grants has to be passed on to you via the reduction in fees - the nursery cannot hold any back.
What you get depends on the number of sessions your child is doing on a set day, usually the 1st day of term, and the grant arrives about half-way through the term. If you increase your child's sessions after the grant has been applied for you will not get any more money, and if you reduce his or her sessions then the nursery has to return the outstanding amount.
If you take the child out of nursery then the nursery has to return the outstanding amount. If you move the child to another nursery, even in the same borough, you cannot get another grant until the beginning of the next term, or whenever it is that the new nursery applies for grants.
And I now know that ds's nursery are being perfectly honest and correct in their calculations, they just can't explain for toffee!