consent to let then maybe buying other house

Hello, just seeking some advice here. I will try to explain all

I recently obtained Consent to let with my mortgage provider, and have a tenant in the house now.

When I was granted consent to let the mortgage provider said I will be free to apply for another residential mortgage if I wanted. I never thought about it at first, but now I am.

So I am asking which other mortgage providers will ignore that I have the other house on consent to let, Are some more lenient than others?

Do I have to tell them about the other house, being consent to let
If the other house became empty I can still afford both mortgages.

advice needed please xx