Is this some sort of community wireless network? Normally wireless providers give you a router to pick it up - I am guessing this is some sort of wireless setup by the caravan park on the cheap?
You could use a wireless extender - something like this
which should allow you to convert the wireless signal into a wired connection that you could then plug a router into to then extend it (or you could just plug a standard switch into it if you trust the wireless
I can't 100% guarantee it would work (and have never actually used that device myself) but based on what you have provided that is my best guess as to a possible route.
EDIT - Another option
if you prefer Netgear...
EDIT2 - A bridge
might also be enough for what you want. This would just convert the wireless signal to wired and then you could plug a router into that to then provide some protection via the nat firewall and use the router to the provide a private wired/wireless network for your devices. The talktalk router may or may not work depending on how much it is locked down but other "cable"/"fibre" routers for around £50+ would definitely work (like the Billion 8800NL).
Edited by ian72 (Thu 29-Oct-15 09:45:42)