I'm a non-British European living in the UK with about £50k in a UK bank account saving to buy a house in Europe. I have a bank account in another European country. With Brexit looming, does it make sense to move over some or most of the money from my UK bank account to my EU bank account? What would be the pros and cons?
As RonJohn said in a comment the main concern is where you want to buy the house. If this is in the UK then keep your money in sterling and if it's in the EU then moving it to Euro is a good idea (although the timing is important).
You need to decide whether you want to buy in the UK or not and that's outside the scope of the question. If you decide to buy in the UK then it is unlikely you will profit significantly by changing your money to EUR and then back to GBP and there's a risk you will lose out.
If you want to buy in the EU then you will need to convert your GBP so the issue is timing the exchange. Markets in general hate uncertainty so I think that it is likely that GBP will rally after March 29th unless the "no deal" option comes to pass (this is basically more uncertainty). If you think GBP will weaken further then exchange now, if you think it will strengthen then wait. Of course it's not that easy to tell which will happen and lot's of people who probably have far more information than you are already trying. If you want certainty then exchange now so you will know for certain how much money you have in the currency that matters to you and not be worrying about whether FX fluctuations will prevent you from buying the house you want.
Well, "worry" fundamentally suggests the need for a hedge.
But there are predictions of the Euro dropping against the dollar and that is based on the European economy slowing down more-so than the U.S. economy.
So an ETF that invests in short-term U.S. bonds would get both into the dollar and also find an interest rate. For instance, the 3-month U.S. Treasury Bill rate is currently at 2.44%.
Or a Forex account based in Euros, and therefor converted from GBP, could then hold an un-leveraged sell-side position in the EUR/USD currency pair and that gets about 1.75% interest after commissions.