YesSo when I invoice I need to add VAT to the allowance element as well as the fee.
Note there are a few specific circumstances where reimbursed items may be excluded - however this can't ever cover anything where you have consumed the service being reimbursed (eg your train travel or your accommodation). an example of when something that may be a non vatable disbursement would be if you collected some materials on behalf of a client that your client had contracted to pay for and you handed across the cash/cheque etc simply as a convenience and were then refunded.
Chapter and verse available here.
https://www.gov.uk/guidance/vat-costs-or-disbursements-passed-to-customers