Didsbury is one of the smartest addresses within Manchester, with prices to match. Areas just outside, like Withington (note spelling) and West Didsbury will be cheaper and nearly as attractive. I wouldn't move any closer to Central Manchester like Fallowfield, Rusholme, Moss Side, Longsight or Hulme as they can be noisier and rougher. I have lived in one of those areas so I know.
Alternative would be to have a UK-based guarantor like a relative (in full-time job and property owner) who undertakes to pay your rent when you can't. They will have to be credit-checked and pass.
You are unlikely to be taken seriously until you actually walk into their office or phone them from within UK, unless they specialise in corporate lets and deal directly with your employer.