Flat Rate Vat query

How can I split a Sales invoice so that only part of the total is calculated as sales turnover for flat rate vat?

For example: My client is an event arranger but also allows other clubs/societies to offer their events via my clients website, my client will then take a small commission and pass the booking fees onto the 3rd party club/society.

For example: My client may have a total sales invoice for £100, but in reality only £10 of this is actual earned income, the remaining £90 will be forwarded onto the 3rd party.

The sales invoice needs to show £100 in total as this amount of money will be paid into the clients bank account, but then the £90 will be paid out again to the third party.

My client used to be on standard vat which meant this was not an issue - i.e Sales invoice of £100 offset against a purchase invoice of £90 - net result £10 income for vat purposes. Now they have changed to a flat rate vat scheme, which means that vat will be calculated purely on sales income - so how can I still record a total income of £100 ( to match with bank statements) but only show the actual earned income of £10 when calculating flat rate vat?