An underblanket sits on top of your mattress.
A mattress cover is 'fitted' in a similar way to a fitted sheet.
Unless you are sure of the thickness of your mattress you should avoid a 'cover' and instead go for a blanket.
Most retail outlets will not exchange or refund your money if you discover that the cover is a poor fit, because of hygiene reasons.
A blanket will fit your mattress, with the proviso that you purchase the correct size of course.
We purchased this one:-
http://www.argos.co.uk/static/Product/partNumb er/4504069.htm
It is very good. Totally flexible, I can have my side warmer or cooler than my partners. The electrics are easily disconnected and the blanket itself can be washed in your washing machine and then tumble dried!
The manufacturer claims it takes just ten minutes to heat up. We can vouch for that - switch it on before you brush your teeth and it's nice and warm for you. It is great on these cold nights, you perhaps don't want the central heating on but nevertheless still want a warm bed.
We told our teenage son we had bought it. He was so impressed with how 'toastie' warm our bed is, we had to go and buy him the single bed version.