Moving your staircase sounds about as challenging as moving your walls. A huge part of your building and its structure, many homeowners will think that moving the staircase is simply unfeasible. But it can and has been done. It will be tricky, lengthy and probably very expensive costing somewhere in the region of £10,000 and £20,000 depending on the size of your home. But it can be done.
You will need to speak to your local building office first to see what advice they can provide you with in regards to building regulations. If you get the go ahead, you should speak to a joiner about moving your staircase and see what recommendations he or she can give. They may suggest knocking down a wall, restructuring the house and alternating the floor plan in order to accommodate for the moving staircase. However, one thing is is for certain: there will be a lot that needs changing if you wish to go ahead.
There are a few other variables that you should be keeping in mind before you commit to a renovation though. You will, of course, have to think about the stairs that are replacing it. Not only where they would ideally be located (and what else would have to be taken down to do it i.e. walls, ceiling space) but how it might look. Would they be made an old-fashioned wood style? A more industrial and post-modern metal one? Or would glass better suit your needs by creating more space and allowing more light to enter the room? You should also think about whether it might be a simple staircase or a bespoke one with a more unusual style.