I have always thought that the high cost of the taxes on buying and selling ones home was great incentive to drive or commute to a new better paying job rather than move nearer to work.
Not living in the millionaire parts of the country I wouldn't know about stamp duty, but the costs of moving house include legal fees and estate agent fees, as well as a removal firm, which can easily reach £5k. Shifting schools for kids (not to mention losing their friends, and indeed your own friends and support network) because your job moved 20 miles are other major non-financial costs, and of course if two people are working then one of you would have to find a new job.
Car based taxes are justifiable on
1) Reducing externalities (mainly polution) which isn't included in normal economic models
2) Paying for roads
Clearly electric cars will be far lower on 1, and very little extra road funding is needed, so if anything money raised by taxes on cars should decrease. A 10p/mile general road charge would be the absolute maximum in that case, so a 30 mile (each way) commute would cost £6 a day in tax and cover the majority of people (average commute is 10 miles)
That's why fares and timetables need to be integrated, reducing those interchange times so the end to end journey is close enough to the drive time to bring it into contention.
That just isn't going to happen in any efficent way.
Say you are a care home manager and get work at Cloverfields Care Home - Whitchurch, Shropshire, and you live 22 miles away near Wyechila Boarding Kennels in Alsager
That's a journey from one fairly large town to another - both which have railway stations, and services heading in roughly the right direction.
it's a 40 minute drive.
The public transport according to google is
walk to bus stop (16 minute)
bus to crewe station (18 minutes)
walk to platform (3 minutes)
train to Shrewsbury (30 minutes)
Walk to bus stop (3 minutes)
bus to whichurch (1h20)
walk to work (1h)
That's 210 minutes even with no waiting.
And why does it need to happen? What is wrong with hopping in your electric car and driving there?
How about Kidsgrove-Winsford? Wilmslow-Winsford? Knutsford to Congleton? In all cases you're looking at most a single bus service between them, which means at least 15 minute walk to the bus stop at each end -- longer than the actual drive, even if free public transport ran every 2 minutes, 24/7, and had a journey speed of 2000mph.
Want to move people from cars for journeys into large cities? Sure, provide parking at stations for free with easy access with half-hourly services from 5am until 1am and free electric transport in the city centre around otherwise pedestrianised areas.
For small towns, increasing pedestrianisation is all that's needed to improve the town, no need for things like park and ride.