I used a free service (London and Country) recommended by Money Saving Expert a couple of years ago - service was ok, a bit slow, mainly communicating by email so this slowed things down a bit.
I paid a local broker (£199) when we moved recently, and had great service, sorted very quickly, and got a good rate on a two year fix (1.41%).
Both options got me much better rates than I would have been able to access if I;d just gone to my usual bank, and saved time, so I think a broker is a good idea.
If you go onto a variable rate at 1.5% it could go up (or down) at any time. If you get a fixed rate, you know you'll be paying that rate (and a set monthly amount), for the period specified. If you fixed now at 2%, the standard variable mortgage rate could rise to 5% and you would only pay 2% until your fix ends.
Keep in mind, if you pay off the mortgage or sell the property within the fixed period, you may need to pay an early repayment fee (usually between 1-4% of the mortgage value). So, if you want to sell in a couple of years, I wouldn't fix for more than two years.