There are a few options nearby for accommodation.
For those with a bit of money, the Solent Hotel & Spa is really nice and it's walkable to the NATS offices. You're looking at £100+ per night.
The Premier Inn is decent. You're looking at £80+ per night and it's not really walkable (but it is cyclable).
The Holiday Inn is very nice but a fair amount of money (varies a lot) and not walkable.
Or I've used this place before:
https://www.airbnb.co.uk/rooms/1908599
It's just a private room on a room-only basis but it's about £45/night and literally a 5-minute walk from the NATS office. Worth a try but sometimes struggle to get availability on assessment days.