Should I ask gp for benefits or housing letter?

I have to submit my pip form soon and all the recent letters I have from my consultant do not discuss how my disability affects me and are mostly non beneficial.

I have been discharged from mental health so can’t ask them to write a letter for me which they previously did. They used to write a good letter for me in this regard.

I was thinking of asking my gp to write the letter(using psychiatrist one as a template) however I have been advised gps are unlikely to write letters for benefits so I shouldn’t. I am also doing a housing application in parallel and was advised to ask for the letter but on grounds it was for the housing application.

I could do this but am concerned she doesn’t do it I’d get desperate and say it was for benefits too but then she might wonder why I didn’t say so before.

Is the advice I have been given correct?
Can you advise how best to get such a letter?

Since my gp is my primary care now(not psychiatrist) and no benefits will have a severe impact on me I would have thought the gp would be eager to help me. Anyway please advise I really need a supportive letter.

Thanks