They may have had something similar, but vaults as they are in the Fallout games were exclusive to America like power armor and FEV are. I imagine that the UK had some sort of nuclear shelters considering that the fear of a nuclear holocaust didn't just pop up the night before the Great War. I'm sure most industrialized nations were taking steps.
We don't need vaults! We have "Protect and Survive"
http://www.atomica.co.uk/
Each UK citizen would have recieved pamplets with the following information:
Planning for survival
Stay at Home
Your own local authority will best be able to help you in war. If you move away - unless you have a place of your own to go to or intend to live with relatives - the authority in your new area will not help you with accommodation or food or other essentials. If you leave, your local authority may need to take your empty house for others to use.
So stay at home.
Plan a Fall-out Room and Inner Refuge
The first priority is to provide shelter within your home against radioactive fall-out. Your best protection is to make a fall-out room and build an inner refuge within it.
First, the Fall-out Room
Because of the threat of radiation you and your family may need to live in this room for fourteen days after an attack, almost without leaving it at all. So you must make it as safe as you can, and equip it for your survival. Choose the place furthest from the outside walls and from the roof, or which has the smallest amount of outside wall. The further you can get, within your home, from the radioactive dust that is on or around it, the safer you will be. Use the cellar or basemant if there is one. Otherwise use a room, hall or passage on the ground floor.
Even the safest room in your home is not safe enough, however. You will need to block up windows in the room, and any other openings, and to make the outside walls thicker, and also to thicken the floor above you, to provide the strongest possible protection against the penetration of radiation. Thick, dense materials are the best, and bricks, concrete or building blocks, timber, boxes of earth, sand, books, and furniture might all be used.
lats
If you live in a block of flats there are other factors to consider. If the block is five stories high or more, do not shelter in the top two floors. Make arrangements now with your landlord for alternative shelter accommodation if you can, or with your neighbours on the lower floors, or with relatives or friends.
If your flat is in a block of four storeys or less, the basemant or ground floor will give you the best protection. Central corridors on lower floors will provide good protection.
Bungalows
Bungalows and similar single-storey homes will not give much protection. Arrange to shelter with someone close by if you can do so.
If not, select a place in your home that is furthest from the roof and the outside walls, and strengthen it as has been described.
Caravans
If you live in a caravan or other similar accommodation which provides very little protection against fall-out your local authority will be able to advise you on what to do.
Now the Inner Refuge
Still greater protection is necessary in the fall-out room, particularly for the first two days and nights after an attack, when the radiation dangers could be critical. To provide this you should build an inner refuge. This too should be thick-lined with dense materials to resist the radiation, and should be built away from the outside walls.
Here are some ideas:
1. Make a 'lean-to' with sloping doors taken from rooms above or strong boards rested against an inner wall. Prevent them from slipping by fixing a length of wood along the floor. Build further protection of bags or boxes of earth or sand - or books, or even clothing - on the slope of your refuge, and anchor these also against slipping. Partly close the two open ends with boxes of earth or sand, or heavy furniture.
2. Use tables if they are large enough to provide you all with shelter. Surround them and cover them with heavy furniture filled with sand, earth, books or clothing.
3. Use the cupboard under the stairs if it is in your fall-out room. Put bags of earth or sand on the stairs and along the wall of the cupboard. If the stairs are on an outside wall, strengthen the wall outside in the same way to a height of six feet.
There's more on the site... Pamphlets on "More permenent" fallout shelters and how farmers should deal with the situation. But the advice is always to stay in your home.
From what I've seen of the UK's real world preperations the advice was always to stay at home - Civil Defense was a local governent issue, as were the immediate aftermaths. If after the bombs you left your home for any reason, you were advised that the area that you moved to would have no obligation to house or feed you, and the home you left (assuming it was habitable) would probably be given to other survivors.
That said, when audits were done, those Councils that complied with the audit generaly showed they were unprepared; Not all councils complied with the audit - some councilors felt that by preparing civil defense they would be encouraging nuclear war.