Do I pay capital gains tax when I sell a rental?

Yes, on the gain rather than the sale price, and it has to be reported and paid within 60 days of completion.

The gain is what you sold it for less what you paid, less buying and selling costs and any capital improvements. Your annual exempt amount comes off what is left.

The 60 day deadline is the part that catches people. It is separate from your Self Assessment return and missing it brings penalties even where the tax was eventually paid.

Rates and allowances are on gov.uk.