Given that taxation is very largely a Member State competence, the potential implications in the UK of an EU exit would be less significant for taxation compared to other areas. The only exception to this is indirect tax (primarily VAT, and to a lesser extent, excise duties) for which there is a substantive body of EU law establishing common rules across Member States.
However given that VAT accounts for 17% of all UK Government receipts, it seems unlikely that any future Government would increase the reliefs from VAT or even abolish VAT, even if they could do so on an EU exit.
For direct taxes, although they are firmly within the remit of each Member State, there is a fairly substantial body of EU case law which has developed to the extent that a Member State has failed to comply with any of the provisions of the EU Treaty (for example guaranteeing the free movement of goods and services across the single market) or has failed to act in accordance with the EU State aid rules. These rules may cease to be of relevance in the event of an EU exit or the courts may refer to the case law in future (e.g. if the UK maintained a free trade relationship with the EU to which these principles were relevant).
There are a number of EU provisions relating to administrative cooperation between Member States to exchange information and help tackle tax evasion. On an EU exit, a UK Government may well seek to maintain some form of agreement akin to these provisions.