Sorry rory but your post does not make it clear and I am sorry to say is incorrect. Your original quote appears to be a mix of the two regs which is misleading for those who do not know.
I'll hopefully clear this up for you. (BTW when you say I cannot work on it I presume you are referring to those not qualified which I am, ACOPs and just done my ACS for the 3rd time). It may help your frustration if you read the regs carefully.
You have quoted were it says that employed or self employed must be of a class of persons approved by the HSE ie. gas safe.
3. - (3) no employer shall allow any of his employees to carry out any work in relation to a gas fitting or service pipework and no self-employed person shall carry out any such work, unless the employer or self-employed person, as the case may be, is a member of a class of persons approved for the time being by the Health and Safety Executive for the purposes of this paragraph.(4) .
However that has nothing to do with somebody working on their own boiler for no financial gain. The only rule required for that is that they are competent, you dont have to be registered to be competent.
This is the reg that refers to the OP.
3.—(1) No person shall carry out any work in relation to a gas fitting or gas storage vessel unless he is competent to do so.
I'm not trying to put you down, but I am worried that people reading these threads may be misled by incorrect information. It is important to the board that incorrect information is cleared up for the readers so they can be informed.