The best place for departures is the port authority, HHA: https://hha.co.uk/live-data/berthed/
They also have a forecast page for incomings, and a departure page when vessels are sailing soon, and an arrivals pages for when they are on their approach.
Port of Felixstowe also have this set of pages: https://www.portoffelixstowe.co.uk/sailing-schedule/shipping-information/
Their predicted arrival times are usually a bit later than the vessel actually arrives, so you are best to use an app like Marinetraffic to keep an eye on them. Larger ships come up the approach channel at 14 or 15 knots at times, so they can arrive very quickly!
Have a good day!