Do I have to log every single shift?

For your tax return, yes: HMRC expects a complete record of your business income, and a partial one is not a record.

There is a second reason that has nothing to do with tax. Your hourly rate is only worth reading if it covers the bad shifts as well as the good ones. Log the three good Fridays and skip the wet Tuesday and JoltMile will tell you that delivery driving pays better than it does, which is a comfortable thing to be told and a useless one.

What you do not need is to log each drop. One shift is one period of work - a Flex block, an evening on Deliveroo, a parcel round. Splitting a round into forty entries buys nothing.

If a shift is half entered when you have to stop, leave it: JoltMile saves it as a draft against your account, and drafts are deliberately left out of every figure until you finish them.