Let's pretend, Mybutty, that you appointed me as executor of your will (but left everything to be shared between your children).
It would be my job to call in all of the assets of your estate, and then use that money to pay all of your bills, your other debts, your funeral expenses and (if relevant) the Inheritance Tax. Then, after I'd done all of that, I'd share out the remainder amongst your children. (Of course, if they'd rather that I didn't sell your house, because they wanted to live in it, they could offer to pay your debts and Inheritance Tax from their own monies. I'd then have to take what they'd paid into account when sharing out the rest of your estate).
So, as you've said, the Inheritance Tax would be paid before your children got anything but (unless they'd voluntarily stepped forward to pay some money, as with my example of them wanting to move into your house, rather than sell it), they wouldn't need to fork out a penny because it would be me (acting as executor) that would pay the Inheritance Tax from your estate.
Of course you might choose to appoint your children as executors of your will. In that cast they'd have to 'wear two hats'. Firstly, as executors, they'd collect in all of your assets, then use that money to pay your debts and the Inheritance Tax. Only then would they share out the rest of your estate between the beneficiaries of your will (who just happened to be themselves). So, once again, the Tax would be paid before any sharing was done, meaning that your children still wouldn't need to find any money 'up front' to pay the tax.