The End of the World is Coming! People have been predicting this for a very long time, and in nearly every year.
Let's say that Global Warming reaches its peak in 100 years. A lot of species will die off because the change is too sudden. But other species will prosper. This is what always happens during and after mass extinctions. This time we have the capacity to freeze the ova or DNA of any animal alive and keep it somewhere safe until we can re-introduce it into a proper environment.
Humanity will see a massive die-off in those areas of the world least capable of handling major changes, such as most of southern Asia and nearly all of sub-Saharan Africa. There will be a mass dying off in the wealthier countries too, but people will survive. We survived the last Ice Age with much more primitive tools than we have now.
In addition to this, many people see a thriving colony on the Moon in 50 years or so and another one on Mars in a hundred years.
The future will be bleak for those who live through it, but everything will stabilize out in 200-300 years.
I don't think the collapse will have anything to do with Britain's service economy. When money becomes worthless, people barter.