At this level anyone with a mortgage would be foolish not to at least consider remortgaging. How long UK base rates will stay so low remains to be seen.
It looks as though, at the moment at least, that UK base rates are more likely to drop a little further than push ahead. However, there is only limited downside left on base rates and you only know the remortgaging rate before you today. What it might be tomorrow, next week or next month is just speculation.
For many people in the UK it is simply a case of when, not if, they will remortgage. However, it is a good point to say that the only rate you are certain of is the rate today. Why take the chance of waiting for a potentially small downward movement in rates?
I dont think mortgage rates will increase greatly in the short to medium term - indeed from what they say there is more chance they could come down a touch further. However, that said the only rate you can guarantee is the one today.