I agree with woofgang. And when you ask, make it clear you have read through your lease and it does not mention at all any prohibition on pets or need to get approval for them.
I'm pretty sure there is no general law about this, but you can check with lease-advice.org if you want.
However, have you & the tenant considered the practical issues? Is the flat on the ground floor? If so, is there somewhere a cat flap could be put in, & do you need permission to do that? If the flat is not on the ground floor how will the cat get in & out? Is there any possibility the cat could be left outside the flat (or able to get out) when the tenant is not there, & then upset other residents? If so, it's likely you would be the one they vented their annoyance on.