Until fairly recently, it would have been sound advice to recommend shopping around for the best annuity rate that you could find. Annuity rates were seriously out of whack with real world life expectancy, so there was a good chance that you'd live long enough to win the 'bet'. However, from what I've heard said in the finance section of the news, recently, these annuity rates have undergone significant revision so, these days, you will get a rate that is - to be fair to the provider companies - more realistic, with respect to lifespan.
If there is a concern that you might not live long enough to get 'a return on your invenstment', so to speak, then you could always pay into a life assurance plan, from the annuity income.
One obvious problem with all of this is that, once you've bought an annuity then you're committed to it permanently. None of us know what's going to happen to interest rates in a few years time, since it's all due to the politics of the moment. The financial advisor might be able to put the numbers into their computer and predict whether it is best to wait or to act now.