Most charging is done at home, work (if lucky) or where you stay (podpoints in holiday parks/supermarkets, parking, even granny cable at friends).
I repeat myself, but when planning a long trip or series of trips, I use A Better Route Planner (ABRP) to plan a return trip (therefore getting a few more charger choices listed out). I click on the table to get a list of stops. I often skip one or more if I know I'll stop for a meal.
The in-car navigation shows stalls available/total. It's the best. Tesla network is the best, but Tesla Model 3 & Y can use any CCS network.
I'm sure you can find a better video - but it shows 7 out of 8 stalls being available. If it was 1 or 2, I'd see if I could skip to next, checking availability. I haven't used superchargers much in UK, but did use them in a continental roadtrip a lot. Only problems were at Leeds (very slow) and busy period in Netherlands when Model 3 sales were VERY high but network wasn't as big as it is now. That one stop in Netherlands at rush hour was the only place I ever saw a Supercharger queue and cars weren't waiting long as there were 16 chargers & most people only charge 15-30 minutes (less nowadays probably, chargers are faster), so you got a changeover every 1-2 minutes. Many superchargers I have visited, I was the only one there.
This is for a new SR, LR would be easier. Charging at Gatwick and travelling slower/more economically (M1 + M25 should do the trick) - probably no need to charge more than once briefly on each leg, possibly no need to charge at all if sitting in traffic a lot (aerodynamics at speed kills efficiency). Adjust parameters to handle weight, weather etc.
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One way with 82kwh Long Range Model 3