I understand you can only 'gift' £3,000 per year to your children, raised to £6,000 if you haven't given them anything in the previous year.
Now, that's not going to go very far towards the purchase price of a modest flat in London.
Bearing in mind that no way is my estate going to exceed the inheritance tax limit even if I pop my clogs in the next 7 years is there any legal way I can give her a bit more than that, say, £15,000?
You have been given the wrong information. There is no limit whatsoever on how much you can give in gifts to one person, especially when there is no IHT issue
As far as I understand it you can give your daughter as much as you want. It only comes back to bite if something happens to you in the next 7 years. If you're inside the IHT limit, death won't be a problem but needing care might.