While the official position of the UK Government is that "Hard Brexit" remains an unlikely possibility given the mutual interests in reaching a negotiated withdrawal, Her Majesty Revenue and Customs (HMRC) nonetheless remains busy drafting rules and guidance which would come into play should the UK exit as of March 29, 2019. Their latest publication is a summary of the main VAT changes that would affect UK businesses post Brexit.
Of particular note, in the event of "Hard Brexit" the UK would introduce a postponed VAT accounting mechanism, meaning that UK VAT registered businesses importing goods into the UK would be able to account for Import VAT on their VAT Return rather than pay VAT at the border. Deferred or postponed VAT accounting is a common technique use to mitigate cash flow challenge associated with cross-border commerce.
The publication, which can be found here:https://www.gov.uk/government/publications/vat-for-businesses-if-theres-no-brexit-deal/vat-for-businesses-if-theres-no-brexit-deal, also contains information explaining how exports to businesses and consumer's located in the EU will be treated as well as the new place of supply rules applicable to the provision of cross-border services.