If a single country used nukes at the start of a great war, everyone who has access to nukes would follow suit. Though i don't think england would be the first one to do this and hopefully no country would be stupid enough to initiate a nuclear attack. A nuclear warfare would mean almost extinction level disaster for everyone.
I guess the most powerful nuclear weapons have a blast radius of less than 100km. So a nuclear warfare doesn't automatically mean the end of all forms of life on this planet, at least for the short term. But in the long term, survival will be difficult, provided how quickly the radiation spreads through air and water.
This is only a theory. The Japanese survived after the nuclear bombings, and Chernobyl disaster. There are many people who never left the area of infection and safely live there still. Animals are also great feeling in there. The effect of radiation is still too poorly understood to speak of the destruction on the planet.