It can definitely be done at 37. Depending on the person of course and your goal (what do you mean by airline?). I have met pilots starting late having less problem than some youngers, because more able to network perhaps... Finding your entry level job without being able to leave the UK, sure it will be a challenge however.
Will my age and eyesight make it hard to secure an airline job?
In itself your personal situation doesn't look that bad (age, medical), problem is the aviation industry now and its future doesn't look that good.