I know a little about this as I live on a canalboat, albeit with a permanent mooring. Its correct that the Canal & River Trust (CaRT) are taking steps to crack down on people overstaying on canals without a mooring, this is generally targeted at people who need to stay in a small area for work, schools etc and try avoiding the need for a mooring by shuttling back and forth along a stretch of canal.
If you don't need to be in a particular area and want to cruise up and down the canals you are using the system exactly as it is intended, and should have no problems with enforcement. Then all you would need is a licence, which for a small boat would be maybe a couple of hundred pounds a year.
Before this I lived on a small sailing boat, again with a mooring in a city centre marina - this is very doable and there are many people living this way, mostly unofficially and under the radar. Living for free at anchor in rivers and bays is a much more difficult prospect, the great british weather can be harsh and at times unpredictable. You would need lots of skills and good equipment, such as an anchor large enough that people laugh when they see it.
I'd suggest the canal option would be by far the best way to start, and you don't need a barge. In central London I see many people on small fibreglass river cruisers, or decommissioned ships lifeboats, that can be bought for a few thousand pounds.
Everything you want to know can be found on
www.canalworld.net