And here's a reply from the Kent side of the river. From Kent CC Planning & Operations Manager, Public Transport
You’re quite right that as of 2nd May a new operator will be in place for the Gravesend to Tilbury Ferry service. From this date, the service will be operated by Jet Stream Tours and they will be using a vessel called the Thames Swift which was previously used on this service. There will be no fundamental change to the service which will run at the same times and charge the same fares and will continue to accept bicycles.
I hope that answers your question but please let me know if you need anything further.
They each have their own perspective. Thurrock calls it "Tilbury to Gravesend" and Kent "Gravesend to Tilbury". Wars have been fought over less.