Is your relative getting Disability Living Allowance or Attendance Allowance? If they are then it makes application for a blue badge much easier. If not they should consider making an application for DLA or AA (which one depends on age) if they can only walk a few yards before experiencing severe discomfort.
With the difficulty in walking that you describe it is worth contacting your local Social Services department for a blue badge application form.
I was going to suggest having a look at
WWW.benefitsnow.co.uk for help with DLA and AA but if you are the same as me you will only get a HTTP Error 403.6 - Forbidden: IP address of the client has been rejected. Anyone else able to browse the site?