Will monthly payments show on Credit Score

Your credit report isn't a full financial report. Its just a record of credit you have had or have available to you.

However as part of your mortgage application you'll likely have to provide bank statements and a overview of your outgoings. Mortgage lenders don't make decisions based on your credit score (the only person who sees your credit score is you and lenders can have different criteria). Mortgage lenders tend to make decisions based on affordability - how much credit you currently have available, how much you're looking to borrow versus how much you can afford to pay back.

If you think you might struggle to get a mortgage then perhaps look at what credit accounts you have open and if there are any you don't use (perhaps a catalogue account or old credit card), then close them.