In the same way gas registration for plumbers (costing a similar sum) has led to a whole army of administrators springing up (called Gas Safe Register) enforcing it, the same could happen for dog ownership with dog wardens running about checking dogs and dog owners for the £375 having been paid.
Also like gas, 1,000 training schools could be set up and a £1500 training fee charged every five years to qualify people to apply for a dog licence. Absolutely loads of new jobs would be created out of nothing which would benefit the economy and everyone.
Granted my proposed dog licence scheme would have no effect on those who ignore it, but then the same happens with the Gas Safe Register scheme. If you check the 'before and after' stats CORGI and GSR have made little or no difference to the number of 'gas incidents' but the behemoth created grinds on regardless. And plenty of people not registered still do gas work with no consequences of any sort.
Blimey that turned into a bit of a rant didn't it!