Brexit won’t affect GDPR. For the uninitiated GDPR stands for General Data Protection Regulation. At the time of writing the UK is still in the EU. GDPR has passed and the UK must be compliant with it by 2018.
After Brexit, the UK can technically repeal it. But will it? No. That would mean EU customer data cannot be transferred to the UK. Imagine how happy UK exporters will be having to move all their servers to data centres in the EU.
I’d expect some kind of privacy shield agreement between the UK and the EU, similar to what they have with the US but stronger. This will guarantee that UK privacy law will remain largely as is.