Hi Dom,
Ecotricity have a monopoly on motorway service areas, apart from some Welcome Break sites that Tesla are now building Superchargers at. Off the motorway, it's a patchwork of regional operators, each with their own infrastructure and tariffs. There is pretty good coverage across the UK. Some of them require you to have a card, some allow ad-hoc payments. There's a helpful summary here:
Public charging networks - Plugged-in Places - Electric cars
But the good news is that you have a top-of-the-range Tesla and the Supercharger network is already pretty good and being improved. You're only really going to have to worry about charging outside Tesla's network if you're travelling in Wales, the Scottish Highlands or maybe Devon and Cornwall or East Anglia. The best approach is to use
Charging points and electric vehicles UK 2016 - Zap Map ,
PlugShare or
EV Trip Planner to find who provides rapid chargers on your route if the Supercharger network isn't convenient.
My guess is that your charging is going to happen in the following order:
1) at home
2) destination charging - at work, visiting family, or a charger at a hotel, restaurant, etc
3) Superchargers
4) rapid charger from another provider
Hope that helps. Are you buying a ChaDeMo adaptor?