Contractor Among Contractors
The HMRC guidance is clear. It's not a disbursement.
But HMRC don't give a hoot on the amount you recharge, just that you add VAT on top.
That means for an original £100+VAT expense, you may charge £100+VAT, or £120+VAT, or anything else + VAT.
The actual amount is a contractual matter.
You can argue the toss with the agency, but really it should be written in the contract, especially if there was an expectation to recharge expenses. The agency might misinterpret VAT rules, but that that's not the same as breaking them, where the actual amount recharged is in question.
Clearly if YourCo generated the invoice it would not say £100 + VAT + VAT.
Just another reason to say no to self billing, IMHO.