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The UK is a joke with regards to governance.
I know a man who contracted a lung problem due to working with petrol motors, he is suffering genuine problems, but works full time and also coaches football, yet he drives a new car, has a new one quite regularily and usually very decent VW Golfs and such, over the years I have seen him with a Subaru Impreza, Golf GTi, Audi A3 sportback, currently has a nice Astra, they are given free for mobility reasons. No cheap tat there, proper new models with all the trimmings. Married, with kids, and a working wife with her own car, bought house! No idea how that works to be honest!
I also know unemployed parents who have been offered mobility cars due to children having slight health issues but unable to take them due to having no driving licence. Not sure why we can't pay for them having driving lessons or if they get GTi's too?
Yet one of my lads has had health problems and regularily needed picking up from school and his mum to be available on short notice, she could not work because of young kids and our son, but because I was working, and even though not earning much or owning a car, we had no entitlements.
Yet we see amputee's managing quite well in dancing, running, and general life with prosphetics? On a serious note, no one is forcing her to do anything, and it looks like she is more mobile than many people I know. Plenty of people dying of cancer and on benefits have to make their own way to treatment on buses.
Can I suggest you read up on the Motobility scheme.
If someone goes for almost any car other than a fairly basic model they actually pay an additional amount for it (even many basic models require an upfront additional and non refundable payment), often a very large additional amount for it.
And IIRC the higher end cars often end up bringing more back into the scheme at the end of the lease (the cars never belong to the driver under the part of the scheme that is most commonly used).
With regards to parents offered the cars when their kids have "minor" problems.
The kids would need to meet the requirements for higher rate DLA mobility component (so not by definition a "minor" problem), now the higher component of the PIP benefit, and it's a fairly standard letter to anyone in receipt of the benefit that says something along the lines of "if you are in receipt of this benefit you may be eligible to turn over part or all of the benefit in return for a lease on a car".
They don't check who has a driving licence as quite often the driver may not be the person actually in receipt of the benefit, but the person that helps the disabled person get around (IE carer). The car has to be used for the person in receipt of the benefit though.
You never get the car "free", it's always in return for you basically giving up the mobility component of the benefit.
It's also worth noting that the mobility component of both PIP and DLA is a non income related benefit, you can get it if you're in work and doing well, or out of work due to the health problems, the idea is that it helps overcome the additional costs of those health issues.
So someone might be making £30k+ a year and be in receipt of it, and they might decide to go for a nicer car than they could otherwise get, but they might only be able to afford that nicer car because the mobility money offsets say the extra use it gets compared to if they were more able, or offsets the cost of them having to have things like stairlifts or wheelchairs and other adaptations around the house that require maintenance.