The following website isn't perfect as two charities have merged and they're still working on it, however I just wanted to mention Serve On (I checked with Fat Rat first), this page has the better pictures:
http://www.serveon.org.uk/community-resilience-teams/The international response section trains teams to send to disasters as rapid deployment teams, such as to locate and rescue people from collapsed buildings in the immediate aftermath of an earthquake. The community response teams project has a broader goal of involving ex service people with communities and transferring skills, mentoring etc.
You don't have to be ex services to assist, they like to mix different skill sets together and there's details on the site if you'd like to get involved. The emergency response section is currently based in Hardwicke, Gloucester, about 80 seconds from the M5.
There's a lot of ongoing costs in training up response teams so if you know a good contact who works in an industry that might sponsor or support an emergency relief team (just little things like for instance, a protective equipment manufacturer who might supply face masks, a hand tools manufacturer, outdoor clothing...), then please drop me a pm to talk (or contact the charity directly).
Thanks
