You can personally build anything as long as you get sign-off afterwards by a 'qualified person'- which would probably be Building Control for the
local council for a new build, but for renovations may be a gas-safe certified engineer for a gas appliance, or a HETAS engineer for solid-fuel stove, etc. The person doing the sign-off is taking on significant liability by signing it off, so many are reluctant to sign off things that they haven't done.
For renovations you can claim 'the house was like this when I bought it'- but without the certificates and 'proof' of signed-off change you don't get credit for the changes in things like EPCs (when you go on to
sell the house, for example). You still get the actual benefits- just not on paper. You may need to get it all signed off to sell the house (depending on what was changed), or pay indemnity insurance for the buyer.
So long as the building is signed off by Building Control or an appropriate person- the house insurance-company won't care who built it. If you make changes that are not signed off then it can invalidate your insurance if anything were to happen to the house- the insurance company would use any excuse to wriggle out of paying!