Great advice here!
Everyone is right. If they are not reimbursing you for fuel, they cannot claim the VAT as it was your expense. If you are claiming fuel or mileage as your expense against your tax, it is not THEIR expense.
However, if they are paying the cost of your travel, then you should hand over the receipts for them to claim the VAT and you should NOT be claiming travel on your tax return.
Again, however, if the £20 allowance (say they are repaying you) does not cover your total mileage costs, you can offset the difference.
We usually advise to claim for mileage rather than fuel/ van costs. Current allowance is 45p a mile for first 10000 miles, then 25p a mile.
HMRC prefer receipts, especially if you are claiming fuel costs, but bank statements can show a paper trail of costs but a diary showing where you were and when is very often used. One of our services is to assist in compiling a mileage log but its far better to keep the record on a daily or even weekly basis. In many cases a site supervisor or contractor can give an account of jobs you were working on.
So, if you are in a situation where they are contributing to fuel costs and you want to claim what they don't give you, I'd personally keep my own receipts and offer them photo copies.
P.S. Just re-read your OP. If you are giving them invoices and you are not VAT registered then they have no VAT claim. And actually, be careful about the fuel you are claiming for... they are paying you £20 if you invoice it as a separate item - so you are in effect being reimbursed travel - or a portion of it. Have you weighed up whether you'd be better off invoicing a single amount (£150 was it), and tell them you will sort out your own travel expense?
HTH... If you need any advice, give Ricky a call on 01280 821020.