We only need to look at EU rates, currently 0%, to see how far UK base rates could fall in theory. Whether they will or not is a different matter but let us not forget that the OECD recently released a report suggesting that the UK economy will perform better than the EU in the short to medium term. This despite Brexit!
It does appear that the EU is coming under significantly greater scrutiny than the UK. We only need to look at Greece and Italy to see what a mess some areas of the EU economy are in.