you'll get a 1 bed flat in Shrewsbury for £350, or £475 for a 2 bed house - 5hrs drive to Edinburgh (petrol is about £1.05 and diesel about £1.10 at the moment), easy access to Telford, Wolverhampton, Birmingham, Stafford etc.. for work, and there's a direct train service to London.
you'll not get squat-diddly in either Edinburgh or the SE for anything approaching £600.
if you need access to both Edinburgh and the SE but can't afford either, Bristol could be a solution - 2 hours from London on the M4, and lots of flights/trains to Edinburgh. 7 hour drive though...