It won't affect your mortgage application at all. When you are applying for credit, a mortgage company will do a credit check. This will let them see a lot of your current credit commitments and how often you pay them.
When I say "a lot of" - the only ones that they can see are the ones that other lenders report. Your rent will not be on the report, so unless you get so late that you attract a County Court Judgement, it will not affect your credit score at all.
Vic is correct generally, but some letting agencies get tennants to sign a credit agreement and could conceivably inform the credit reference agencies, your score could then be affected. Did you sign a consumer credit agreement when you started renting?
Having seen CAIS data for both Experian and Equifax forover 4 years I can hand on heart say that I have not seen a single bit of CAIS data from a letting agent.