This fine piece is known as King Dick's bed. It was brought to Donington from Leicester, where it stood for many years in the Blue Boar Inn. According to its previous owners it's the bed that Richard III slept in on the eve of the Battle of Bosworth. (Where he died for want of a horse and ended up buried under a council car park.) However, it's just the base and the rope supports that might have even a distant connection to the king. The canopy and tester all date from the mid 17th century. (And the curtains are only a couple of years old.)
Beds like this pre-date spring mattresses, of course, and bedding was supported on a web of ropes that could be adjusted by pulling hard on them from the sides. (You can see the loops in the photo.) This is supposedly the explanation of the expression "sleep tight".