"Wipe out" is indeed what it would do.
Let's imagine this is a MIRV with 15 separate warheads, totaling 50 megatons, total (maybe). Let's imagine the targets are the following British cities: London, Bristol, Plymouth, Portsmouth, Birmingham, Sheffield, Liverpool, Manchester, Leeds, Newcastle, Glasgow, Edinborough, with the larger ones receiving two warheads.
Britain would basically cease to exist as a nation. So much damage would be done the economy would be non-functional. All the transport links in the country flow through those now destroyed cities, and that infrastructure would be destroyed. Every single piece of modern electronics in the country and in neighbouring countries that was not EMP hardened would no longer work, and everything (especially the transportation system) depends on all this stuff working. The prevailing south west winds would ensure that enough fallout would end up on surrounding areas adding to the casualties, and areas with nearby nuclear power stations would receive a lot of extra fallout. Just feeding the survivors with a barely functioning transportation system would be a logistical nightmare - ground transportation would be difficult thanks most of the major road and rail routes having been destroyed. Injured survivors would be left to fend for themselves - the entire capacity of the health service would be overwhelmed with the casualties of just one of the bombs. The electricity grid would be destroyed, even to the undamaged areas, it would be years before power was restored.
The survivors themselves, many of them would be suffering PTSD in the years afterwards, and virtually everyone will have lost friends and family and probably most of what they own in the attacks. What survived wouldn't be Britain, it would be a grotesque almost zombie like Britain with at best third world conditions for decades following.
Just because there are survivors and some land left untouched doesn't mean the country is effectively destroyed.