Hi,
If you are based in the UK and you are providing a service for a company in the EU then if this service comes under the genertal rule of services then the supply will be outside the scope of VAT. You can see see the guidance below:
The place of supply rules for services
If you are charging on expenses then the expenses should take on the same liability and so would also then be outside the scope of UK VAT.
If the supplies are outside the scope of UK VAT then there would be no requirement to register for VAT in the UK.
Please see the guidance below:
Working out whether you need to register
Thank you.