UK Government grant for charging station

The government is kindly offering to pay 75% of the installation costs for a private charging station. They have a list of approved suppliers here:

Which one would be the most suitable for charging the Model S?

Wait and see what the confirmed hardware is for the S. If it has a 32A single/3Phase charger built in and a 62196-2 socket then most on the list will be suitable. If you want/they offer twin chargers, 63A single/3Phase then you are a bit limited. Wait and see.

Would be interested to know, do Tesla install their own charges for customers?

?? a charger is a rectifier built into the car, to allow it to take AC feed and turn it into DC to charge the battery. A Model S can have one or two built in. Each handles about 10 kW. You can have Tesla add the second if you just purchased one initially.