The UK is a hotbed of some of the best brand work on the planet. The climate for strategists, especially freelance ones, is very good. What you have to understand is that brand strategy is still relatively niche (there is only a few hundred of us strategists globally) so you can command decent day rates and work with some incredible brands on some brilliant projects.
What I would say is that working abroad is always a good idea – and it does not matter how long for. I spent six months in New York freelancing for a branding/packaging agency when I first went freelance and the experience could not have been better for me. It opened my eyes to how different cultures and consumers thing and act, this in turn has influenced how I think about brands and projects now I’m based in the UK again. Since then I have worked on projects in 14 countries around the world and these experiences have made it easier for me to get new gigs as I am able to adapt to lots of different markets and consumers.