Short answer is that you can do ALL of it - and yes that does include the gas.
In general, building regs don't restrict WHO can do the work, only to what standard it is done. Also, whether you can do the work, and whether it is notifiable, are two different matters.
For the electrics, if you are competent to design and install the system, then you can do so. You are still required to meet the same standards as a professional should be working to, but you are allowed to do it. As part of the overall project, it's probably not going to cost extra to notify either. For minor (notifiable) works, it's often more expensive to pay LABC fees than to get someone in - my LABC charges about £150/£225 for minor electrical works (the different prices are for whether you can supply acceptable test results or whether it will need an inspection), while a member of an approved scheme can self notify for a few quid.
Much the same applies to gas. You still need to work to the same standards, but there is nothing in law which prohibits you working on your own system - ie you aren't doing it in any way for a consideration (ie it's not trade).
Naturally, whether you are competent to do these works entirely without outside assistance/oversight I cannot comment. Both electrics and gas have obvious and not so obvious dangers, and it would certainly be wise to work with someone who really does know what they are doing.
The building regs lay down the standards you need to work to. Schedule 4 lists what isn't notifiable - basically, work down the list, and if you find a statement that says you don't need to notify, then you don't (and stop there, don't read any further). If you reach the bottom of the list without finding such a statement, then the work is notifiable.
