I do not think DIY should be regulated beyond requiring that the person doing the work "is competent" (which is what the laws pertaining to UK gas plumbing state)
England and Wales went through this in 2005 with the introduction of "Part P" of the Building Regulations. Basically anyone doing electrical work that is notifiable (most major work) must either be registered or must report the work to the Building Control dept of the local council for a fee. The councils generally don;t know how to handle this so mostly just get an electrician in afterwards to perform a full system test for another fee making, say adding a new circuit cost around £200-300 in fees alone.
Prior to the introduction of Part P the government's own stats for England and Wales stated there were around 5 deaths per year from fixed electrical wiring. It notes a further 25 possible deaths due to fires where the fire was due to an electrical source of ignition but that does not break down into fixed wiring vs appliances and extension leads. Most informed sources estimate the number of deaths from fixed wiring directly or by resulting fire to be around 10 per year.
The number of deaths on the road in the GB was 1901 in 2011. Scale that back a bit to remove Scotland.
Do I think limiting who can do electrical work is a waste of resources? Yes I do. The resources would be far better spend on road safety.
To require being a member of an accredited institution to do water plumbing (with the possible exception of sealed heating systems) is even more laughable.
There is a difference between regulation and limiting electrical and plumbing work to members of a closed shop artisan/union style which seems to be the case in Australia and becoming the case in the UK.
 I am legally allowed to do my own gas work in England, provided it is "not for hire or reward".