Typical timing after the tax year
Interest in P800 timing usually rises after the tax year ends because that is when people expect HMRC to review records and issue calculations. GOV.UK says tax calculation letters are sent between June and March of the following tax year, and the online tax calculation service says HMRC calculates everyone's Income Tax between June and November. If you need the wider background, start with the full P800 refund guide.
That is why timing pages often become more important from late spring onwards. People are not only waiting for letters; they are also trying to work out whether their case has been handled yet or whether it is still too early to expect anything.