There are 2 cities, Bath and Wells. The county town is Taunton and other towns include Yeovil, Weston-super-Mare and Bridgwater.

Somerset County Council

Bath and North East Somerset - Bath, Keynsham.

Bath - Lansdown Park and Ride BA1 9BJ - Spaces for motorhomes. No height restrictions. 878 spaces.
Bath - Charlotte Street - recommended for high vehicles. A large open air car park within the city centre.

If you are visiting Keynsham with a tall vehicle then we recommend using the following car park:
Bath Hill East  - This is an open air car park with no height restrictions, all the bays are standard length. It is located within a short walk from the high street.
Please be aware, if you need to straddle two or more bays within a car park due to the size of your vehicle, you will need to buy a ticket for each and every of these bays.  If the vehicle overhangs the bay and is outside of the parking area then it will be liable for a Penalty Charge Notice.

North Somerset Council - Weston-super-Mare, Clevedon, Portishead, Nailsea

The above link takes you to the car park location page of the website.

The only car parks to be used by motorhomes are the following:-
Weston-super-Mare - Melrose car park, Knightstone Road, BS23 2BE - designated bays only. 270 spaces. Please read the cp notice board. From Peter The spaces are extremely limited, tucked away in a far corner. Do not park in any other bay where you take two spaces. Cost could be £50. Read the notices closely. PS. JF has told me Melrose now has a height barrier.
- Salthouse Fields, Old Church Road, BS21 7TU - designated bays only. 250 spaces. Please read the cp notice board. This cp has a height restriction of 2.1m. Gain access through coach gate by calling 01275 884 700 and request the padlock code. It is your responsibility to maintain safety for pedestrians and other vehicles! This from the council website.
Weston-super-Mare - Beach.
No overnight sleeping is allowed in any of the councils car parks.

Mendip District Council - Shepton Mallet, Frome, Glastonbury, Street, City of Wells.

There is no specific parking allocation within Mendip for caravans and motor homes (with the exception of Clarks Village), although they are welcome in most of our car parks providing payment is made for the number of spaces occupied. (The 1525 kg weight limit primarily applies to commercial vehicles only.) Parking is not allowed in coach or bus bays.
Dedicated caravan and motorhome parking is available at Clarks Village. This parking is located in the car park off Southleaze Orchard, Street. Customers wishing to use this facility should follow the signs from Southleaze car park.

The above website specifies whether motorhomes are allowed or not. The car parks below are the largest which allow motorhomes. They are all p & d.
Frome - Cork Street BA11 3JB - 65 spaces. MH allowed - yes.
Frome - North Parade BA11 2AB - 87 spaces. MH allowed - yes.
Frome - Cattle Market - 339 spaces. MH allowed - yes.
Frome - Merchants Barton BA11 1PT - 68 spaces. MH allowed - yes.
Shepton Mallet - Commercial Road BA4 5BU - 131 spaces. MH allowed - yes.
Wells - South Street BA5 1SJ - 40 spaces. MH allowed - yes.
Wells - Union Street BA5 2DZ - 149 spaces. MH allowed - yes.
Wells - Tucker Street BA5 2HG - 71 spaces. MH allowed - yes.
Glastonbury - Butt Close - 74 spaces. MH allowed - yes.
Glastonbury - Northload Street BA6 9JJ - 35 spaces. MH allowed - yes.
Glastonbury - St John's BA6 9JJ - 142 spaces. MH allowed - yes.
Glastonbury - Norbins Road BA6 9JE - 53 spaces. MH allowed - yes.
Street - Cranhill Road BA16 0BY - 316 spaces. MH allowed - yes.
Street Clarks Village - Southleaze BA16 0BJ - 272 spaces. MH allowed - yes. However, if your vehicle takes more than one space or is likely to overhang a space and block or partially block a pavement, you MUST NOT use this car park. It is NOT administered by Clarke`s Village but by the local council who actively patrol it. PS. UPDATE from SC. Parking is allowed in the staff car park next to the fire station. Call in advance (01458 840064). On arrival call to let them know you have arrived.
Street Clarks Village - Grange 1 BA16 0BY - 368 spaces. MH allowed - yes.
Street - Northside BA16 0BJ - 245 spaces. MH allowed - yes.
Street - Southside BA16 0HY - 106 spaces. MH allowed - yes.
Street - BA16 0BN - free car park. MMM mag.

Sedgemoor District Council - Bridgewater, Burnham-on-Sea, North Petherton, Highbridge, Axbridge.

The car parks below are the largest in each town. There is no mention of height barriers.
Bridgwater - Mount Street East - 115 spaces.
Bridgwater - Mount Street West - 93 spaces.
Bridgwater - Northgate - 162 spaces.
Cheddar - Church Street - 64 spaces.
Cheddar - Cliff Street - 129 spaces.
Highbridge - Bank Street - 109 spaces.
Burnham on Sea - Good parking roadside. There is a 4.5 m max length but when we were there a number of MH parked roadside. There is a good turning circle at the end.Apparently the car park on the front has spaces but I cannot confirm that.
Burnham-on-Sea - Pier Street TA8 1BT - 16 bays for mh. There are 3 cp here, East, South and West. West is short stay. Adjacent town centre. MMM mag.

South Somerset District Council - Chard, Ilminster, Somerton, Wincanton, Yeovil, Castle Cary, Crewkerne, Langport, Milborne Port, Bruton, Martock.

The link above takes you to the car park page of the council.

Please note that no South Somerset District Council owned car parks allow motor home parking at this present time.

Ilminster - Sports and Bowling Club TA19 0RG - At Donyatt, Chard Road - overnight £6.50. Showers available. Saturday car boot sale. Sunday carvery. MMM mag.

Taunton Deane Borough Council - Bishop's Hull, Comeytrowe, Norton Fitzwarren, Taunton, Wellington, Wiveliscombe. (Will merge with West Somerset in 2019)

Taunton - park and ride - Silk Mills TA1 5AA - no height restrictions. PW
Taunton - park and ride - Gateway TA3 5LU - no height restrictions. PW
Taunton - Motor home owners are advised to use Tangier Car Park (TA1 4AS). If a motor home takes up more than one parking space a Pay and Display ticket must be purchased for each parking space used. The Phone and Pay parking service is not appropriate as it automatically takes payment for one parking space only. PW tells me parking in the town centre is rather tight.

Owners should note that Council bye-laws do not permit sleeping overnight in car parks.

Wellington - Longforth Road TA21 8RQ - 158 spaces. No height restrictions. PW
Wellington - North Street TA21 8LZ - 99 spaces. No height restrictions. PW
Wellington - South Street TA21 8PW - 83 spaces. No height restrictions. PW
Wiveliscombe - Croft Way - 78 spaces. No height information. FREE.
Wiveliscombe - North Street - 45 spaces. No height information. FREE.

West Somerset Council - Minehead, Watchet.

The car parks below are the largest in each town.

Minehead - Alexander Road TA24 5DP - 102 spaces. No height restrictions but has a narrow entrance. It says suitable for motorhomes but be aware of the narrow entrance.
Minehead - Seafront/Warren Road On Street Parking - 290 spaces. Suitable for motorhomes.
Dunster - Dunster Steep TA24 6AS - 109 spaces. Suitable for motorhomes.
Kilve - Kilve Beach TA5 1EG - no spaces or height information. MMM Mag.

All other car parks in the council area are unsuitable for motorhomes.