It will have a negative impact on your application, but hopefully not negative enough to rule out the new mortgage that you need. This is because banks do a stress test on your existing mortgage (as rates could increase), and they discount your rental income (as there are taxes and other costs associated with renting, and rents can fluctuate).
You mentioned that the rent "just about covers" the mortgage, so the stressed mortgage will be higher in their calculator, and the rent will be lower. This will create a double deficit in their mortgage calculations, which will lower the maximum mortgage available. In effect, it is treated the same as if you had a short-term loan of the same amount a this deficit.
The various banks treat these calculations quite differently, so you will probably get a wide range of mortgage amounts from the lenders. This is one reason to shop around, or to speak to an independent advisor.
Best Regards,
Dave Curry, Irish Mortgage Corporation
https://ie.linkedin.com/in/davecurryirl