Just to demonstrate how ignorant I am in these matters, what's an annuity and how would I know if I've got one?
An annuity is what your man in the street refers to as a pension, i.e. a monthly/weekly payment which is made to you. The pension is the pot of money you build up during your working life.
For example, let's say you reach retirement age and have built up a pension "pot" of £50,000. This pot will be held on your behalf by a pension provider (eg. Aviva, Standard Life, The Pru etc) and will usually be made up of your contributions and your employer contributions (plus the tax savings). At that point you have a number of options, you can take some of it as a tax free lump sum (typically max 25% although I think you can take more if your pot is small), you can take that money and put it into a Self Invested Pension Plan (SIPP), or you can do what most people seem to do, and buy an annuity with it.
An annuity is basically a contract between you and an annuity provider (which could be the same company that holds your pension pot, but it typically pays to shop around). The contract says that, in exchange for your £50,000 they will pay you an amount (say £75) per week/month for the rest of your life. The annuity provider will take into account a number of factors (age, weight, smoker, general state of health etc) to make a guess at when you'll die and then calculate how much money it'll pay you based on that. Basically, if they think you'll be dropping off the perch before the end of the decade, you'll get more money than if they think you'll see 100.
For clarity's sake perhaps the following should be made clear :
During the accumulation stage of your pension 'life', someone (you, your employer and/or the govt) pays into your pension "pot". As you change jobs you may accumulate several different "pots" with different employers. You can usually keep these all separate, or opt to merge them into one larger pot - it's up to you. The value of the pots will grow or fall in line with the assets held in the pots - stocks and shares, funds, bonds, cash etc)
When you come to retire, you can chose to buy an annuity with some or all of the assets contained in some or all of the pots. An annuity is a contractual promise (usually with a big insurance co) to pay you an income for the rest of your life. Once you buy an annuity, the money/assets in the "pot" is gone - to the insurance company. You can't get the money/assets back, and you can't sell or surrender the annuity for cash in the future either. On the other hand, the insurance co can't stop paying you the promised income till you drop off the perch.
Prior to about 2006, just about everyone had to convert their pension pots into annuities. However, nowadays there are many more options, and many more flavours of annuity too. AIUI less than 50% of people now buy an annuity with their pension pots. However, it's still true that once you've bought an annuity that's it - your pot of money/assets is gone.