There's a Daido Juku dojo in Slough:
http://www.kudouk.com/kudo-training-venue.html
never been there though so can't tell you how good it is.
As somebody mentioned there's Shidokan in London:
http://www.shidokan.org.uk/
Also since recently, Sensei Darren Stringer (3rd dan Kyokushin
http://darrenstringer.com/) is giving "MMA Karate" lessons at easyGym in West Croydon. I haven't been to those classes yet but heard good feedback from one of my instructors, and I had the chance to train with Sensei Stringer a few times in the past and it was very technical and informative. Sempai Alan Shnawa assists him there
(
https://www.facebook.com/alanjshnawa/info)
For actual Kyokushin, if you want a really tough dojo I recommend Bethnal Green dojo, with Shihan Graham Warden (6th dan) and Sempai Kenny Jarvis (2nd dan) as the main instructors. The dojo has had some great success in knockdown tournaments with names like Nick Da Costa (placed 6th at the World Tournament in 1984 when it was still only one united Kyokushin organisation), Darren Chan, Kenny Jarvis, and Timmy Warden (only ever Brit to win an IFK World Tournament).
It's my dojo (even though I haven't been able to train there for the last 2 months) and the toughest in London in my opinion, you will go home limping and bruised more than once ^^
If you're interested it's closed in August but back in September. The website is down at the moment but here's the Facebook page with address and training schedule:
https://www.facebook.com/pages/Bethnal-Green-Karate-Club/444352388999076?sk=info
Other dojos I tried and liked are Docklands dojo with Shihan Da Costa as main instructor (
http://www.docklandsdojo.co.uk/), Tokei dojo in London Bridge (especially the fight club on Sunday morning which is basically 1 full hour of knockdown sparring), and Crystal Palace.
hope that helps