Disregarding war, climate change does not look good for wildlife, it is happening to fast to allow for habitat transformation.
And I am not sure what wildlife would like an even more wet and windy UK.
I agree that climate change is too fast and that many species will be lost because of that. However, habitat destruction by humans is an even bigger threat than that. The problem is, of course, that climate change is likely to accelerate habitat destruction by humans because we'll need new places to live and grow crops when the current ones disappear.
My expectation (crystal ball) is that these pressures will result in major wars that will set us as a species back hundreds of years or more. Human population will collapse and in many areas nature will take over again, like what happened in Tsjernobyl or Central America. This hasn't happened on a global scale yet, but there are many examples in history where locally people wiped themselves out by not taking enough care of their environment. Currently, we are so dependent on global systems (energy from the Middle East, electronic parts from Asia, food from all over the world, data from offshore datacentres that can be destroyed in a major war - much of our knowledge lost, because who writes paper books nowadays?). So if this falls apart, many areas won't be able to survive. And the areas that do survive will be set back centuries because of the unavailability of resources and the knowledge that was lost.
Imagine most of our electronics gets destroyed by an EMP during a major conflict and global supply lines are cut. That's the end of civilisation as we know it. People will kill each other over the few remaining resources and most will die, ending up with just a few pockets where people survive on sustenance farming. None of these pockets will have knowledge or resources to rebuild what was before. Nobody knows how to design and produce a transistor, let alone a microprocessor. So we are going back to the iron age, more ore less, with population numbers to match. Then, nature will start reclaiming the earth.
We are currently living in the middle of a mass extinction event. We will end up with a greatly reduced number of species, but some of them will thrive in the new environment. Hopefully the few species-rich nature areas that still exist can serve as a starting point when they get taken over by nature. Like the little hills that you come across in the jungle of Guatemala, which are actually cities that were reclaimed by nature hundreds of years ago after the human population wiped itself out. It's going to be awesome.