Currently self-employed UK citizens have the right to work in any EU member state, but how would a shift to Brexit impact this?

It really depends on the negotiations by British Government with EU nations, and personally I do not trust the likes of Boris Johnson and Nigel Farage to do such negotiations on our behalf, but in short Brexit would almost certainly take away or at the very least limit our freedom and flexibility of movement among the EU, something that we take so much for granted. The Guardians full article here.

Vote remain, vote in! Happy voting today people!