Building surveyor for legal purposes?-uk

I've had severe issues with my rental house and have been waiting months for my solicitor to arrange the building surveyor to attend to look at it.

Can I hire my own surveyor and pass on the report to a legal team?

If so , does anyone have a rough idea what it would cost?

It's mainly to inspect damp, I'm guessing the surveyor they have lined up wouldn't be doing anything more than a basic damp reading, although they aren't clear exactly what he would be doing.

I have evidence of damp readings myself but apparently it isn't counted as evidence if I'm not a surveyor.