£100 is not terribly high, especially for London.
Break it down
£10 shipping either way so £20
The connectors I could not get just anywhere but
https://eu.mouser.com/Connectors/USB-Connectors/_/N-88hmf?P=1ylqy95 starts getting there, from a later link I see it could be a bit more custom though.
Call it £5 as it will likely be a special order. If I have to do something like
https://www.alibaba.com/product-detail/power-socket-charging-port-dock-connector_60680894915.html and buy a minimum of 10 I am not going to expect to do many so be prepared for more
Laptop power jack replacement
https://www.alphacomputers.co.uk/laptop-power-jack-repair/ is £69 all in.
That's a laptop though. This is probably closer to a mobile phone, not amazingly different in terms of skills required.
https://www.ifixit.com/Teardown/Nintendo+Switch+Teardown/78263 says as much if I am looking at it.
Some places seem to be offering £30 or so for phones, one even offering £20 something for a DS port. Interesting twist.
Anyway if it is to go on my bench I would wonder what the damage was. Normally for connectors it is years of abuse or being dropped when charging. Something going in there that should not is second on the list and can be both easier and harder than the former.
Three main scenarios in repair
Straight surface mount desolder and replace. Nothing major.
Trace repair. Annoying if you know what you are doing but nothing too taxing.
Fuse repair. Someone shoves a pin or something in the connector, shorts something out (or causes pins to permanently short) and if there is no fuse/current limiting the fun may never end, or may take a little while as I then get to check components and do a proper test at the end.
My bet is Nintendo would do a motherboard swap in this scenario but that is not a luxury we have at this stage in the game.
Hmm, maybe take it a phone repair shop with a copy of that ifixit link or printout or something and ask.
Complete cowboy option.
Integrate one of those wireless chargers to the battery. Does not skip the issues with fuses and shorted connectors either but if we are playing a cowboy who cares. You would also lose anything that goes through the connector. Such a kit (without the charger anyway) is less than £10 and can be soldered directly onto wires and only requires a minimal disassembly.