I suspect that there could be a hybrid solution where you pick your charging system.
Option 1 (highest cost, all miles at 12p per mile plus VED of £150 per year plus congestion charges at the day rate) you pay for the miles your car records you undertake only by means of the mileometer on the dash and congestion charges on the day rate controlled by ANPR.
When you register for this system you pay a £200 deposit which is returned when you log the car as sold with a milage which is confirmed by the buyer any dispute over milage is charged to both parties. MOT garages can confirm milage at any time (they would probably charge), when buying/selling a car privately people would likely do this to limit their liability.
MOT garages which provide mileage which is suspect would be investigated and potentially have fines applied. However they would also have to take a photo and it be backed up to the cloud (like Google photos) with the time/date data included using a DVLA app which also logs the time/date as well as the MOT garage.
ANPR could also provide estimates of miles traveled.
Option 2 (mid cost, you pay for each zone you enter or exit, plus congestion charges) you pay for zonal travel controlled by ANPR. For example rural A road passing through 5 villages means you pay for each of the 5 village zones plus for each of the A road zones between each village, whilst a large town would have major road zones and residential zones, each zone you pass through adds another charge (typically between 5p and 95p per zone, although some rural zones may be free to enter or exit but you are charged if you pass through).
Option 3 (lowest cost, miles are charges at between nothing for rural areas through to 20p per mile, however there's no congestion charge fees), you run an app on your phone or car and it charges you for the miles traveled, ANPR used to check the app is recording miles traveled by means of pairing vehicle references.
Vehicle references are linked to location data (ANPR, GPS or miles logged at MOT), no individual would be able to cross check between location data and end user details as vehicle references are then paired (through another system) to an account reference (only providing time/mileage/cost values), which is then in tern paired (through another system) to payment accounts.
Payment accounts pay the value against a time. This would allow companies to pay for work travel milage whilst staff are requested to pay for personal travel, depending on the agreement this could be directly to the payment account with visibility of time/milage/cost data or by staff submitting a given time/milage/cost value to their accounts department.
As the payment accounts may not actually be the person making the journey (i.e. husband pays for his and wife's travel); all knowing who paid does is know that they have an interest in that journey.
On the back end, staff should be within Chinese walls, so no one person can access the data across all three systems. Although they may be overall oversight of the systems those with that oversight do not have permission to request data. Some may have the ability to see data between two systems but not all three, such data checks would be logged as abnormal requests.
Whilst there would be edge cases where option 2 might work out cheaper on some days (i.e. someone driving between a few urban zones a lot Vs paying a high per mileage rate on the tracked system) generally people would be best off with option 3.
It's then up to them how much they are willing to share that data to have a reduced payment.
Some insurance companies could offer per mile insurance if you allowed them access to your time/milage (but not cost) data.
Payments can be taken automatically each month.
Penalties for speeding (average speed check over a length of half the square of the speed limit, so 450m for a 30 rising to 2,450m for a 70) could be applied, with small fees for small over speeds (say nothing for average speed being +3mph, +3mph to +6mph being 50p, then for each 0.5mph above that it doubling the fee; so +6.5 would be £1, +7 £2, +7.5 £4, +8 £8, +8.5 £16, +9 £32, +9.5 £64, +10 £128, and anything of +10mph or more being a court summons).
In addition for every 2mph above +10mph would earn you one point on your licence plus 1 point (+10 would be 2 points, +12 = 3 points, +14 = 4 points, etc), so go an average of 32mph over the limit and you earn 12 points (so doing 62 in a 30 limit or 102 on a 70 limit).
However if your accrue £150 in fines with a value of £2 or more in any 12 month period you'd be sent on a speed awareness course, more than £300 and you'll do the course again (unless you've already done 4 within the last 3 years) and more that £1,500 in a year or be eligible for that 5th speed awareness course within the last three years and you'll get a court summons.
To rack up £300 at £2 a fine would be 150 offences (or 3 a week) where your going an average of +7mph. That's not a mistake, that's a pattern of behaviour. Especially given the person would have been on one speed awareness course already once they racked up £150.
The app would show you speed limit, real speed and average speed, with a warning colour (amber) shown at +3mph and a further warning colour (red) at +6mph.
Whilst that'll mean those opting for option 1 or 2 are still at a lower risk of being caught speeding (although ANPR could also pick up average speed checks for speeding) their ability to speed would be limited by the fact a lot of people around them would be sticking to the speed limit. However, fines for being caught would increase, with their being tiered fines as their recorded speed gets higher. The fine would be a minimum of double of the fee for others. They would only have one option for one speed awareness course per year and that would be at a national level rather than per police force. They would also be subject to a minimum of 3 points on their licence.