if you’re getting a Model X you probably won’t mind. My boss got one for his Model S, money wasn’t an issue.
Huge sweeping statement to extrapolate Your Boss to everyone who spends £100K on a car is money-no-object on things such as wall chargers
I am told that there is only about 20-24 amp room on the board. Will that be enough? Any idea what it might cost to run a new, dedicated line from the city mains to my garage? (about 100 ft)
I suspect you are taking a USA view ... UK wiring is a bit different ... so "best guess" I think you will be fine.
Most houses have some high power draw items - such as cooking hobs and ovens. They aren't on all the time. UK homes don't have AirCon / Furnace big-electricity-users (but your UK home might ...)
Your house might have electric showers - i.e. heat the water "instantly" at the Shower, rather than heating a tank of hot water and circulating that round the house to the tap / shower. If your house has several of those, and teenage kids, then you may be near the limit (when everything is on).
But even then you are most likely to be charging your car overnight when those are all off ...
And if it really is a problem then you could have a device to turn the car charging off when there is other high-load in the house (as described above)
As mentioned above:
We have 13AMP 240V sockets around the house (different to the rest of EU, and definitely different to USA - your phone/laptop will charge faster on 240V than it did on 110V
). In the UK there are no high-power "drier sockets" [i.e.using 2 phases?? I think in USA] in the garage, or anything equivalent; so we just one single phase to each house and a loop(s) of 13 AMP sockets around the house.
High power items like Cooker have a dedicated, fat!, cable (and no plug/socket, they are hard-wired into a junction box type thing)
So a wall charger, outside, is basically like a cooker - dedicated cable, 7kW device
13AMP charging speed = 6 miles per hour (might be enough? certainly OK for "fall back" / temporary / visiting friends).
7kW Wall Charger = 22 MPH
13AMP is less efficient (i.e. more losses) than dedicated wall charger.
Typically wall charger cost is £450 - which is the same as the Grant (if you get an OLEV approved device)
Installation cost on top is about £400 unless long cable runs / complicated
UK Tesla comes with UMC cable with connector for 13AMP and also Commando (so you could fit 7kW Commando socket at your house instead of wall charger, but you would have to use your UMC cable, increase the wear-and-tear on it, and if you need to take it with you have to coil it up and put it in the trunk each time, even if it is wet, raining and miserable ...). personally I prefer a tethered cable on a wall charger.
Is three-phase power so uncommon in the UK for a home?
Yup, very rare, and because power company has a monopoly is often extremely expensive to have fitted, even if the 3-Phase is available at a pole-in-the-garden (not uncommon for connection to be £5,000 - £10,000)
In UK we typically have 3-phase available down the street, house 1 = Phase-1, House-2 = Phase 2, ... House-4 = Phase 1 ...