What happens if my Eurostar service from Brussels is running late and I miss my Grand Central train from Kings Cross
It depends on your train ticket from Kings Cross.
In the UK, there is a special train station called London International (CIV) and London Eurostar (CIV). If you book a domestic train ticket from this station, then any connection with an international train is guaranteed under CIV rights. That means that if you travel to London and miss the Eurostar, you are entitled to take a later Eurostar, and to hotel accommodation if the later Eurostar is tomorrow. Conversely, if you travel to London and miss your UK domestic train, you are entitled to take the next one and, if applicable, get hotel accommodation or a taxi if you missed the last train.
International trains means either the Eurostar or the train+ferry to Harwich-Hoek van Holland.
For more information, see the UK connections page on Seat61.