Bedfordshire is covered by 3 unitary authorities: Bedford, Central Bedfordshire and Luton. Besides Bedford other large towns include Biggleswade, Dunstable, Luton, Whipsnade and Woburn.

Central Bedfordshire County Council

Central Bedfordshire website gives the following information:
Only three of our car parks allow sufficient access and manoeuvrability to accommodate motor homes. All of our car parks are covered by Traffic Regulation Orders which contain height restrictions and a requirement to park within a bay, however the following car parks will make exceptions (including relaxed height restrictions) for motor homes provided the following requirements are met:
where a motor home cannot fit into a single parking bay due to its length, the driver must purchase two pay and display tickets for the two bays occupied
no form of camping, sleeping overnight or cooking are allowed. There are no facilities for these activities.

Dunstable - Ashton Square LU6 3SN - 387 spaces access from West Street via St Mary's Gate only.
Dunstable - Grove Park LU5 4JD - 437 spaces access from Court Drive, parking at the rear of Go Bowling.
Leighton Buzzard - Duncombe Drive LU7 1SD - 139 spaces access from Lake Street.

Bedford Borough Council

There is no information for motorhomes. Some cp have height restriction.
Park and Ride - Elstow MK42 9XF in Progress Park on the A6 at A6/A421 jct.. No height or size information.

Other car parks. No height or size information available.
St Peters Street MK40 2PR.
Greyfriars Street MK40 1JD.
Ashburnham Road MK40 1DW.
Duckmill MK42 0AU.
Borough Hall MK42 9AP.
Melbourne Street MK42 9AN.

Luton Borough Council

The Parking and Enforcement Plan 2013 for Luton states that all car parks have height restrictions. I have enquired from the council if this is correct and could they do something about it for us motorhomers. The answer was no the height barriers will stay 'to prevent unauthorised encampments'. There was no recommendation for where a motorhome could park instead a phone number to call 'for assistance in relation to parking a larger vehicle'. The number is 0158 254 8523.