Initially they'll just use the mileage on the MOT to send you the tax bill for the year. Now you know why they've put the MOT records online so it's already available for their tax reporting.
https://www.gov.uk/check-mot-history
Eventually all cars not 'classic' will be lease owned by the manufacturer and you'll just pay a weekly/monthly cost to use it. Mileage will be tracked as part of the lease and fed to the government so the tax is included in the regular charges.
Though that's too simple for the government, so they'll spend billions upgrading all the roads to 'smart' ones so they can track number plates and charge toll fees.