and perhaps put a garage CU on the end rather than feed it into a socket as it is now.
Probably no benefit. What size cable, and what is protecting it at the source end ? Unless it's some unusual combination, putting it directly into a (BS1363) socket is perfectly fine as the fuse in the plug will provide protection for the plug, socket, and appliance cable - and if the circuit is correctly designed and installed then the upstream protection will protect the cable run.
Many, many installations are nothing more that a spur, with one or more "13A" sockets on the end, and a fused connection unit (FCU) for the lights - usually a switched FCU so it provides both the down-fusing and switching in one accessory.
However, the trouble with the legislation, as written, is that, strictly speaking, it seems that one is meant to provide the first EICR to the tenant (if there is one)
If there is a tenant in-situ then one is supposed to supply
each EICR to them. If there isn't, then it's perfectly OK to only offer the latest.
, and to to LA 'if requested'
I do have to wonder how often they ever ask for one unless there's something else going on to attract their attention ?
, with no apparent provision for a 'second' (or subsequent) one - and that that 'first' EICR triggers a requirement for all C2s (and any C1s) to be remedied within 28 days of that EICR.
A second (or subsequent) EICR is sufficient to prove having dealt with any C1 or C2 defects on the earlier one. And if you read the regs taking each EICR in isolation, it makes more sense.
I.e., each EICR you have done, you have to provide to any existing tenant (and the LA if they ask for it) - if there isn't one, then you don't have to give it to anyone (I think, not even the LA if they ask for it as at the time the property doesn't have a tenancy.) If you are taking on a tenant, they only need the last one, and once the tenancy has started and the regs kick in, then you would only be bound to supply the latest one to the LA.