If the money you're collecting and passing on to the client definitely doesn't count as turnover that would have to go on your own VAT return, then it should just be a case of creating another dummy bank account in QuickFile for "client money" or whatever you want to call it. When you collect money from a customer you tag that as a transfer from "client money" to your collection account, when you pass money on to your clients (less the fee) then that would be a transfer the other way. This will leave the "client money" account overdrawn by exactly the amount of your fees, which you then account for with a sales invoice that you mark as paid into "client money" to bring that back to zero.
This is essentially the mirror image of what you do when you take payments via a merchant account like PayPal and receive the money net of the payment handler's fees - in this case you are the handler.
But given there's VAT involved I would definitely talk to a real accountant and/or HMRC about whether the money you're collecting actually counts as turnover that you'd have to charge VAT on.