When my wife was forced into buying an annuity when she retired we faced the same issue as the pension fund holder will usually push their preferred option for obvious reasons.
We eventually contacted Hargreaves Lansdown, as we were existing clients, gave them the details and they came up with 3 companies for consideration. We eventually opted for Just Retirement and went with the fixed income option.
Whoever you opt for they are bound to ask a certain number of questions regarding your circumstances and health as they wont be able to give you an accurate quote on basic details. Given that this is a one time only choice you need get as much info as possible before making a decision which you wont be able to change at a later date. We spent a couple on months evaluating the details given to us.
I was lucky enough not to be locked into an annuity and its not a route I personally would go down given the current rates. My wife was lucky in that she managed to get in just before the rates started to plunge.
By the way I am not making a recommendation for the companies mentioned, just relating our annuity experience.