Disabled Persons Rail Card

Good evening forum users.
This is my first ever post, and I am looking for some advice.

I suffer from chronic back pain and find it very difficult to walk long distances or stand for prolonged times.
Anything over around 10-15 minutes can leave my back in quite some pain.
As such I plan my day so that I do the minimum of standing around or walking for a long time.

I don't drive, and I rely on my local train to get me to and from work, however I have found that recently, the volume of passnegers has shot up and I have been finding it impossible to find a seat anywhere on the train. I have tried taking earlier and later trains in the hope that they might not be so busy, but this has not worked.

I asked a rail staff employee what I should do and they suggested that I apply for a Disabled Persons Rail card - I am a little unsure of how this would help me find a seat, but none the less, I have contacted the company who provide these but I don't appear to have anything which they would accept as evidence I have a disability. I don't claim any benefits and don't really intend on doing so whilst I am able to get to and from work.

Can any users suggest what I can do from here?

Thanks
Harry