It's really difficult. We're the opposite to you, have never fixed, so have always been better off. But the way interest rates have behaved in the last 10 years has been unusual.
I don't see interest rates going up much in the short/medium term. There's too much personal and business debt and it would fuck the economy.
One thing you need to consider is the impact of fees, some mortgages have huge fees, so they charge a lower interest rate to make it look cheaper. Changing every 2 years is likely to cost more in fees. Divide the fee by 24/60 months to see the effective cost per month.
There are advantages and disadvantages of short and long term fixes and no-one knows what the right decision will be and the other thing is that, the longer the fix, the more chance that something will change in your life that makes you want to get out of it (another DC, job change, inheritence, bereavement, divorce etc) and getting out of a fixed rate can be expensive.
In your circumstances, I would probably take the 2 year fix, but save the £120 in a savings account earmarked for the sole purpose of being available should the next mortgage in 2 years time if it is more expensive. If it is, you have money to help you pay it, If it isn't you have nearly £3k of money to spend or overpay the mortgage with.