The UK will continue to have a VAT system after it leaves the EU and the VAT rules for domestic transactions will remain the same.
There will be various changes in the VAT system, some are as follows:
Businesses which are VAT-registered and currently trade with the EU will be automatically issued with an EORI number allowing them to trade with customers and suppliers in EU member states following Brexit. Businesses which are not VAT registered will need to register for an EORI number in order to continue their dealings with EU member states.
According to the HMRC, after Brexit UK companies will no longer be able to use the UK’s VAT Mini One Stop Shop (MOSS) service to declare sales and pay VAT due in EU member states. For sales made after Brexit, UK businesses will need to register VAT MOSS in any EU member state.
UK businesses will be required to register to the VAT of a member state supplying them goods.
Similarly following Brexit VAT triangulations and other EU VAT simplifications will no longer apply to businesses which are only UK VAT registered.