Brexit will have certain implications for taxation in the UK. Some aspects will be more particularly affected, such as VAT, whereas other taxes could be more indirectly affected. Of course, this all depends on how the UK actually deals with these taxes and also how any agreed system of VAT or parallel form of it is agreed between the UK and remaining EU.
VAT is an EU tax and has been imposed in the UK since accession in 1973. It is subject to EU directives, and although there are a number of individual state derogations, treatments and rates, the underlying system and alterations to it are EU in origin. Due to its revenue generation, VAT will not be abolished. However, its operation for importers and exporters could be affected. How UK exporters deal with VAT applying to both business and end consumer customers in the EU will need to be negotiated as part of a Brexit agreement. Also, non-EU exporters thinking of operating through an EU entity (such as for electronically supplied services) will need to monitor how any UK/EU agreement deals with services arising from the UK.
Direct taxes, such as corporation and income tax, are not subject to EU regulations and directives. However, the underlying principles of the EU such as freedom of movement of capital have impacted on issues such as loss relief (eg the Marks & Spencer case), as well as the treatment of distributions. Also, State aid rules have been used to ensure that unfair tax benefits are not conferred on favoured or domestic businesses. Initially, one may think that leaving the EU could allow greater flexibility for domestic tax policy (in that freedom of establishment principles and State aid rules may not apply). However, any trade deal with the EU may mean keeping these rules (and future EU interpretations) in place. There are also other international principles (such as from accounting boards and the OECD) that are promoted by the EU and which would generally be expected to apply to the UK in any event, as they would be applied by international convention.