Great answer from QuentinUK. I would add that you should be aware that although you do have access rights on footpaths, many of them go through private land. Some land owners maintain routes and signs better than others, but if they have made the effort follow the path as best you can. Sometimes these routes are for getting you across safely (especially in working farms - yes you may find yourself in a field of cows!), some are to help maintain the land owners privacy.
Whilst it is safe to trek alone in England, just be wary if you want to cross areas like the Yorkshire Moors or Dartmoor. Weather in the UK can be cold and wet, and onset of fog can cause you to get lost. If you do want to disappear into these areas for a few days make sure you have proper supplies.
If you haven't seen it already, I'd recommend reading this web page from the Ramblers UK - lots of information about access rights, routes, and suggested equipment.
Have a great time!