can you paddle on open water in britain without permission - not unless it's classed as an ancient navigation (ie historical), land owners either side of the banks own half the river bed, so as such in law they control access to the water.
can you travel up and down canals without a form lakes - You need a British Waterways licence for canals, this is included in the BCU membership fee.
can i purchase or build a canoe and paddle any were if not whats the rules? - you can paddle in the sea (and true tidal rivers) no problem, trespass in a canoe is a civil matter so it's not a police involving incident, though still illegal. Problems occur where arrangements have been made to allow canoeing at certain periods and this is broken by paddlers, mostly this relates to well fished areas as paddles sports are peceived by fishermen and landowners (those earning cash from selling the fishing rights) to be damaging to fish stocks, which is a load of rubbish.
Try the BCU website above as it tells you loads, it may also be worth searching the BCU site to find a local club who will be able to help you.
John