Am I entitled to the minimum wage as a delivery driver?

Only if you are legally a worker or an employee. The National Minimum Wage and National Living Wage do not apply to somebody who is genuinely self-employed.

Which you are is not settled by what the contract calls you. Tribunals look at how the work actually runs: whether you can turn work down, whether you can send somebody else in your place, how much control the platform has over how you do the job, and whether you are really running a business of your own.

This has been fought repeatedly in the UK gig economy and the outcomes have not been uniform. Some private hire drivers have been found to be workers; some courier arrangements have not.

If you think you have been misclassified, it is an employment tribunal claim and there are strict time limits, usually three months less a day from the act you are complaining about. Get advice early. ACAS is free and is the normal first step.

Being a worker for rights purposes does not change your tax position by itself. Tax status and employment status are decided separately, which is confusing and is nonetheless how it works.