You only need to check the existing as far as your new work depends on it and you are not introducing a danger that wasn't there before, or instance (In terms of pre-lim checks)
Change a light fitting - Check there is a Zs at the point you are working and verify that the circuit is not on a supidly sized circuit breaker
Add a new cirucit - Check the suppliers earthing arrangement, bonding, that there is a suitable way to come off
Adding extra sockets to a ring - RCD to ring? Ring is continous and the the point you are comming off is on the ring
etc.
Also remember that the regs are not retrospective, so if you are asked to change a socket and its not on RCD, you can do that and just note it down, the point was there without RCD protection, and it still is, but if you are asked to put another one at the side of it, you have fitted an extra point that wasn't there and that must comply. A broken socket shouldn't be prevented from being swapped out just because its not on RCD.
In terms of testing when finished, a minor works is possibly overkill for an accessory swap, you could just have a custom form that documents what you did and what the zs was, along with rcd times if it was on RCD and you wanted to.
If you are there to change a light fitting and notice something that would be a C1 on an EICR then you should make the person in charge aware, and ideally (as long as they don't object) do something to remove the immediate risk, so if the problem is a totally smashed socket, then taping it up and labelling as out of use would be considered reasonable, then make a note of it in comments on existing, but you might find that they just ask you to swap it and add it to the bill.