I wouldn't on both principle and practical grounds.
Principle
This is supposed to be a free country. We regulate the entry and practice of certain professions, like Law, Medicine, Gas work and HGV driving because there are overwhelming public safety reasons for doing so, and therefore the vast majority of the public support those regulations. Whilst there might be a valid argument for putting oil on the same level as gas, I certainly don't see that general plumbing falls into this category, and more importantly, neither does Joe Public.
Practice
I don't believe it would achieve what it sets out to achieve. If the public don't believe regs are necessary, they will simply ignore them, and pay their mate from down the pub. In the unlikely event that you could enforce it, we would then get every other trade, profession and pastime seeking regulatory protection for themselves. I would start a campaign to regulate merchants, to make sure that I didn't have to deal with any new competition.
So every extra £1 you earned because you were a licenced plumber, you would have to spend £2 because you were no longer allowed to do your own carpentry, plastering, tiling etc, or maintain your own vehicle, or even cut your kids hair. The only people who would make money from it would be the regulatory and training agencies.
By far the most valuable thing the government could do is get the HSE to properly prosecute all instances of unsafe and unregistered gas work. If we can't properly enforce our existing regulations, we have no business introducing new ones.