An EICR requires the inspector to do a lot of work, which is not required if the result is a re-wire.
I only really needed to remove one ceiling rose cover, to see the rubber cables were crumbling.
It will take maybe an hour to fit a consumer unit with no outputs, if that, it is the putting of each circuit into the consumer unit which takes time, so think mine was fitted in around 6 hours, so you're throwing away 5 hours of work if you fit a consumer unit then have a re-wire.
There is also the point if it needs a re-wire then the electrician can't really power up any circuits.
I have had this argument with a code C1 with an EICR, it should never exist, as if that bad, it should be isolated, and once isolated it is no longer a code C1.
So really needs a more honest approach. Be honest with the electrician, so you ask, will you have a quick look first, and say if you think it will need a full rewire, as hardly worth doing an EICR if it is clearly going to need a full re-wire, if it's not going to need a full rewire, then do the EICR to work out which bits can remain.
OK, we can take it as read it will need a new consumer unit, but the main point is how it is going to be done. Mothers house as it was by time it was rewired, would be re-wired cheaper if she was not there, well in real terms no option, could not do a re-wire with a person with alzheimer's in the home. She was in a care home while it was re-wired, which mean speed was a big thing due to cost of care home.
My son put his family in a caravan in the garden while it was rewired.
If the re-wire team need to make it safe each night, it will cost more. The same applies if they need to keep a supply on to a freezer, some may have generators or power banks to bridge the gap in supply, others will not.
Also decide what you want, no good asking one to also run internet cables and the other not, I would get a price on a basic re-wire, if you then decide you can afford more, that's OK.
Decoration is another thing, a painted wall is easy, a papered wall is far harder, so with the papered wall the socket was in the corner, technically not permitted, but trunking down the corner does not look too bad, down the centre of the wall it would look quite bad.
Even the two way switch in the bedroom needs considering, pull switch over the bed is quite easy, chasing down to wall with a bedside lamp and switch each side of bed is clearly more work, and a smart switch with Alexa means you don't need two way switching, consider all this first.
I use Nest Mini speakers, and voice commands for a lot of my lights, some have smart bulbs, some have smart switched, one has a smart relay, asking for deep back boxes to take smart switches, or neutrals taken to switch to power a smart switch, or neutral to light to power a ceiling fan, now is the time to think about it.