It might tbh.

I wanted to be one but I think they would be very cautious about putting someone with a mental illness in that position

Best thing to do is take a walk to your local station and talk it over with one of the officers there, theyre usually happy to chat.

If you're in the UK perhaps apply to be a special constable

Lol, a "Special Constable?"

Dude, if you pass the psych tests you are home free... I wouldn't even mention the BP unless you are directly asked....

They do not want people on meds carrying a gun. Go to the fired department. You will not pass the psych test.

Talk to your psychiatrist about this? Who knows? It might be possible though suspect it would an issue?

I did... And was a good police officer until I chose to do something else...

I try to avoid any inherently stressful kind of work. I wouldn't want to be a cop running around with a taser and a gun, but that's me. And if you're like me your interest in being a police officer will pass and you'll be on to something else. How about being a social worker or parole officer? Those jobs are also stressful but in different ways.

I know the psyche evals are tough and they can request your medical records.
I actuallly qualified for a dispatch position but cracked before the final qualifiers.
I have been working as a DPSST Officer for a reputable security company for a year and a half or so now and I love it.
The FD suggestion was good! I use to have my EMT and worked with a dept and I loved all of it! Not to mention the eye candy LOL. sorry could not resist