Do I pay tax on rental income?

Yes. Rent is taxable income and you declare it through Self Assessment.

You pay tax on the profit rather than the rent, so allowable expenses come off first. What is left is added to your other income and taxed at your normal rate.

There is a property allowance that covers small amounts of property income, and if your rental income is genuinely tiny you may not need to declare it at all. Where you sit depends on your own figures, and an accountant will settle it faster than a search will.