Hi @Marmot,
I'll take care of this query for you about multi-currency transactions.
Given that the client in question is recorded in your QuickBooks Online (QBO) company as a customer that pays in EUR, and the supplier as a vendor that you pay in GBP, then you can follow this process: Enter billable expenses.
Create a bill, that's billable to the client. View the screenshots below for reference:


At this point, you can create the invoice for your client. Check out the screenshot below for reference:

Be advised, you'll have to input the exchange rate for each transaction. 1 GBP for USD, then 1 EUR for USD as well.
In case you want to undo a billable expense assigned to a customer, see this article: How to remove a billable expense charge.
I'll be around to help if you need further assistance. Tag me in the comments below, and I'll get back to you.