The UK pound has fallen since BREXIT although perhaps not as far as some expected. It could fall further, especially if a "hard BREXIT" becomes more probable.
I am no financial expert but I could imagine the euro losing a lot of its value in 2017. The Eurozone has some hard times ahead: Greece is very unlikely ever to be able to pay off its debts. There are strong right wing (anti EU) forces in many European nations. It would not surprise me to see the euro tumble. I may be very wrong, but the signs are there.
As for the UK, I think in the end we will be OK. I voted "remain", but there is a lot wrong with the EU. There is a lot wrong with the euro too: the idea is right but all nations need to be in step and abiding by the same rules as if they are in one nation. Greece should never have adopted the euro in my view.
See http://www.bbc.co.uk/news/business/market_data/currency/default.stm .