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.