I am in the middle of remortgaging and have been wondering the same thing. I think the consensus opinion by the people who know more about it than I is, the economy is (in the short-medium term) going to be screwed. Brexit might work for the better in 50-100 years, but it'll be bad for this generation.
Unfortunately this doesn't answer the question about base rates. We've seen them keep base rates down to stimulate the economy, but conventional thinking is that if inflation goes up (which with no trade deals, we can expect to see all our food etc go through the roof) then putting interest rates up combats this.
So it could stay low, or go high. And it's gone very high before. 15% in the eighties to try and curb inflation - it worked, but I wouldn't fancy paying 15% on my mortgage.
After umming and ahhing for a while we've decided to fix for 5 years. We might lose out, but lets face it, interest rates aren't going to go down (or by much), but there is a reasonably high chance they could go up significantly. We did the sums and it works out at a loss of about £3K to us if rates don't go up over that time - but given we've been fixing for two years the last few times, that is actually wiped out by saving on setup fees etc.