... testing the fixed wiring installation using an Earth Loop Tester, an RCD Trip Tester and an Insulation Tester, none of which can be used to test portable appliances(PAT)
You also missed testing the CPC (circuit protective conductor) by measuring the resistance.
As electricians tend to use a combined "all in one meter" that always include resistance and insulation why can't these be used to test domestic appliances?
You don't need a dedicated meter with these functions when you already have the measurement capability within you're existing test equipment. Clearly you don't have a nice mains socket on the tester to plug into but this is easily overcome (even ready made adapters are available for this function).
Permanently installed domestic equipment can also be tested using "standard" electricians test equipment since PE and insulation can still be tested.
In all cases testing should only be performed by those who are competent and in the case of testing electrical installations you will also need to be suitably qualified (Part P or BS 7671 , e.g. via City & Guilds 2393-10 or 2382).