It depends why you are downgraded and what job you want to do, for example:
If you have knee problems that prevent you tabbing that is irrelevant in most jobs in civvy street so it will have no impact (if you want to get a job as a sherpa obviously that might be a non-starter).
If you are graded MND because you can't walk then clearly that does impact on many jobs - although in terms of application process it impacts in a positive way rather than a negative one. Disabled candidates are guaranteed (by law) to be offered an interview (under the guaranteed interview scheme) for jobs which they apply for, (providing they are suitably qualified- if you have no qualifications and apply for a job as a Doctor you will not be allowed an interview). Employers must take reasonable steps to facilitate the disabled candidate being able to work there, and cannot factor in the cost\imbuggerence of making changes to the workplace when determining who will get the job. This means a prospective employer cannot turn down the disabled candidate on the basis that they would have to do things such as install new ramps, buy a new desk or similar such thing.
This means that disabled applicants cannot be filtered out at the 'paper sift' and thus allows you the chance to come across well at interview, which many former soldiers will as they (generally) have a decent level of self-confidence.