You have a number of issues here:
1. Can you park on the street?
2. Can your tenancy be terminated for parking on the street?
3. Does the council have to make any allowances for disability access etc.?
Number one:The Highway Code sets out where parking is/not allowed, and where it is suggested that you do/don't park:
https://www.gov.uk/guidance/the-highway-code/waiting-and-parking-238-to-252 .
Basically, yes. Unless you're causing an obstruction of the highway, other restrictions, you can park on a road.
Does it matter where you park on the road? It can do. Preventing someone from
leaving their property is obstruction of the highway (although preventing them getting back onto their property is not). This will depend on your facts - if the garage owner can in fact drive out of the garage onto the road then the parked cars haven't caused an obstruction. From what you say, the road is easily wide enough; but it may depend on how close to his 'access' the cars are parked and the angle of travel.
NB. I agree with other that the garage owner is breaking the law by driving over the kerb and grassed area (and is there a pavement too?) to access / leave his garage, unless the council has given him permission to do so pending installation of a dropped kerb. You could therefore argue that he has no right to enter or leave the garage using a car in any event, as to do so involves breaking the law. But two wrongs don't make a right …
The Property Ombudsman has agreed in the past that it appears to be the law that people can park across properties where there is no dropped access:
https://www.tpos.co.uk/news-media-and-press-releases/case-studies/item/an-undropped-kerb-misleading-action Number two:As Aunt Sally mentioned earlier, it may depend on what is in your tenancy. If there is a clause that says Thou Shalt Not Park on That Road, then the council can probably argue its point. But I doubt you have such a clause.
There might be something in the tenancy about not breaking any laws. However, even if you had such a clause then you'd be within in your rights to say that the council can't terminate a tenancy unless you've actually been convicted of breaking the law … which of course wouldn't apply as the council hasn't prosecuted anyone.
Finally, there might be something more vague in the tenancy about generally being a good egg, or not affecting neighbours. The council could have a bit more leeway with this one.
Number three:The council has a duty to provide allotments, but - assuming it has access to the land around it - does not have a general duty to provide access to them other than on foot with a wheelbarrow. It also is not obliged to provide parking. The council agent is right so far.
However, under the Equality Act 2010, where a particular way of doing things places a disabled person at a substantial disadvantage to those without the disability, then there is a duty on someone providing a service to make reasonable adjustments to reduce or remove that disadvantage.
Equality Act 2010(That is why blue badge holders are exempted from having to comply with certain local parking byelaws for up to x hours - the council's bye-laws / practices would cause a substantial disadvantage to people with disabilities, and a limited adjustment is reasonable to ensure that they can access the local facilities. It is not an unlimited right - blue badge holders are not allowed to park at all in certain places, where an obstruction or danger would be caused, and for only a certain duration).
The council agent is therefore completely wrong in principle by saying they don't have to make any allowances for people with disabilities. If a practice of theirs puts people at a substantial disadvantage, they have to make reasonable adjustments. Note that only reasonable adjustments are needed.
There is also the Public Sector Equality Duty, where public organisations such as councils must have due regard to the need to 'advance equality of opportunity between persons who share a relevant protected characteristic (e.g. disability) and persons who do not share it'. Again note that they must 'have due regard to'. They are not required to take any and all steps that might assist.
https://www.gov.uk/government/publications/public-sector-equality-dutyOn your site, what does that mean? I'm not sure that it would be reasonable to make all paths wheelchair-accessible, for example. It has to be proportionate. Ditto for providing a toilet.
I also don't think that they can do anything legally about the specific parking situation for blue badge holders, unless they put yellow lines along the road and only allow BB holders to park there or create a designated space on site as suggested by someone (I realise there isn't the space to do so now). If the parking on the road is, in fact, causing an obstruction then there's nothing the council could do - that law is a national law and therefore a council can't give someone permission to break it in this way.
Sorry, this has turned into an essay. I hope that at least some of it was understandable and useful! At least it might give you some ammunition in the rather high-handed way this council agent has dealt with the situation so far.
Do you have a local ward councillor who might help you? Also bear in mind the Local Government Ombudsman has certain powers once any complaints route with the council has been exhausted. But do try to persist in resolving this informally if you can - take photos of the site, have a site visit, to see what the parking in reality is like etc. I agree that they are likely to think that it's easier to shut you up and appease the garage owner...