Can I be charged to tow tenant’s car?

If the car is parked on private land then insurance and tax is not required. The owners of the private land have their own rules which they inforce. However, if the car is in your parking space then surely they would only consider towing it away If you said you didn't want it there. So if you have asked the management service to remove it- then it won't be done for free. I would suggest that once you have the invoice that you then invoice the tenant responsible, I expect there will also be storage charges that the tenant will need to pay to get the car back. The tenant might be better selling the car to a scap merchant if they no longer want it, write to the tenant explaining the charges and their liability. The tenancy document you have used should clearly state the parking rules and the result of ignoring them so the tenant can't say "I didn't know-- you have stolen my car"

move it onto public highway?

Refer to the Lease regarding leaseholder parking rights/restrictions and freeholder enforcement.

I've been through this before and it basically boils down to this: a vehicle can be moved by one of three entities: the owner, the local authority or the police. Anyone else removing this car without a court order or the owner's permission will be committing an offence.

If the owner is not cooperative, there are still two institutions that might help. The police will only remove a vehicle if it's on a public highway as opposed to private land. Getting it there is a bit of a problem that could have different solutions.

The local authority will intervene if the vehicle is abandoned and thus present an environmental hazard. The checklist to consider a vehicle as abandoned include broken windows, flat tyres, signs of fire damage, rubbish inside and absence of number plates. Any two of those will likely trigger some interest, again, getting there is another problem to solve 😉

Despite what alocjtoi says which does not provide a solution as basically, like he/she said, police & LA won't do anything, in a similar situation I notified the car owner that unless car was removed within a stipulated period it would be removed by XXXXXXX scrap merchants which I arranged. Any costs involved would be passed on to the owner or any value in the car said scrap merchants were prepared to pay would go to the owner. Additionally any necessary repair to the car space resulting from dropped oil etc would be billed to the car owner.
There may be howls of horror to what I've said but it worked for me!

Reply to the comment left by Richard Adams at 15/05/2021 - 13:42Yes, this would work if the owner is not aware of the legislation. Otherwise he will successfully sue for damages. Most of the car scrap companies will refuse to take a car without a logbook, as it's basically a theft, but I do know one company that would not care.
All this ordeal is a grey area that's very difficult and time consuming to do right, but there are ways around here and there if you are prepared to bluff or cut some corners.
P.S. I am providing a solution, but you'd need to read between the lines.

This article summarizes the legal position: https://www.askthe.police.uk/content/Q441.htm
The options suggested are court order or civil action and that's pretty much all legal options available unless the car is dangerous. That is, if the owner is not willing to cooperate or succumb to threats.

Reply to the comment left by alocjtoi at 15/05/2021 - 13:59
Likelihood of car owner being aware of the possibility of sueing for damages is remote and even if they did unless the car is a spanking model of some expensive make rather than a clapped out banger worth little which it likley is, what damages can they sue for anyway? As long as records of ultimatum notices to the car owner are kept for production in court no problem. Won't happen though most likely. Like i said it happened to me over a year ago and had I not acted as I did the offending car would still be sitting there.

set light to it?

Reply to the comment left by Richard Adams at 15/05/2021 - 14:11
Yes, your suggestion is very good and could work. Also costs next to nothing, so very worth implementing. Unfortunately I've been in a position where this hasn't worked as the offender was quite aware of the legislation and actively resisted all my efforts. In the end I was lucky to avoid a criminal charge as the said legislation is hugely unfair to landlords. Not that it's of any surprise though.