From recollection for DIY plumbing for water and waste is unregulated, all gas requires registered fitter sign-off and electricity is mixed. You can change sockets, light fittings nad the like (because, as you say no would know anyway) but alterations and additions to circuits have to be signed off by a registered person.
For the regulations, a competent person is a qualified, registered and regularly checked tradesperson. Of course, part P makes a mockery of all of it all.