I think both @Redflagsabounded and @Thatsanotherfinemess1 make very relevant points that you should consider further.
"Do you have a legal right of access across their car park?"
This will likely appear in the original deeds to your house. If you still have a mortgage then the lender will likely hold them.
"...for over 30 years"
I guess from this that you probably no longer have a mortgage. If that is the case then it may be that the original deeds have been returned to you or the solicitor who acted for you at the time.
Alternatively, as it may be that the property was only first registered when you bought it (presumably in the 1990s), they may have also been sent to HM Land Registry who will have digital copies.
You can search here:
https://www.gov.uk/search-property-information-land-registry
If the register for your property refers to deeds being "filed" then they should have digital copies of the original deeds.
If the deeds mention a right of way over that land, then other people cannot block your access.
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The second issue is, have you obtained rights to use the land anyway?
"If you've been using the access for 30 years you may have acquired a right of way (easement)... If other neighbours also have previously used it for access a joint letter might carry more weight."
However, this can get very complicated indeed. If you want to go down this route then I really would, very strongly, suggest that you first speak to a solicitor who is very experienced in this area of the law.