Depends a bit on your tax band. You have to pay tax on interest you receive (unless it’s in an ISA) but there’s no tax relief on your interest payments, so that tends to favour paying off your mortgage. The rates on cash ISAs tend to be pretty miserable – unlikely to be more than your mortgage rate. An investment ISA might beat your mortgage rate, or it might go down in value.
Definitely look at an offset mortgage, but when I was last remortgaging, it made no sense due to the higher rates. The higher the ratio of your savings to mortgage balance, the more sense it makes.
Worth reading the small print on your mortgage, it may be more flexible than you think. On mine, I can make 10% overpayments each year, but I can also then take a payment holiday up to the value of my historical overpayments. So if you’re worried about losing your “rainy day” fund by overpaying your mortgage, you may find that you can get some of your overpayments back if it really does start raining, albeit not as a lump sum.