Looking at your sizes there, it seems to be a standard 5ft bed. (the bedding industry still work in feet and inches as most of their machines are old)
But I would make sure when you ask.
Then you need to know what type of mattress you need. There are so many variations from £80 to £1000.
If you don't have any special needs, I would highly recommend a pocket sprung mattress. The comfort level is the highest.
I got one for a friend and his words were (after a few weeks of using it) 'it's like snuggling down into a little nest'
I have a king size double pocket sprung mattress with a single sprung base. It would have cost £1200 but I got it for free
as I worked there often and saved them money with a program I did.