Eurostar trains from King’s Cross St Pancras have also been unable to reach the Netherlands due to the poor weather.
Passengers travelling between London, Rotterdam, and Amsterdam are being advised to postpone their journey.
“Please don’t come to the station if your train is shown as cancelled,” a statement said on the Eurostar website.
“We regret that trains that can run will be subject to severe delays and possible last-minute cancellations.”
This follows Eurostar services being hit after a power supply problem caused significant disruption in the Channel Tunnel last week, leaving thousands struggling to travel ahead of New Year’s Eve.
Heavy snow is still causing disruption to trains across northern Scotland, with Network Rail Scotland warning “exceptionally deep snow and severe weather conditions” are limiting the progress of its snow ploughs.
LNER has advised anyone travelling between Edinburgh and Aberdeen not to travel until 14:00 GMT Tuesday.
Severe weather is also affecting services in Wales and trains are disrupted between Wales and Manchester Piccadilly as well as between Llandudno Junction and Blaenau Ffestiniog.
Stagecoach has suspended all bus services in Aberdeen and Aberdeenshire until further notice “in the interest of driver and passenger safety”.
In Shropshire, firefighters trudged through half a mile of snow in the dark to deal with a chimney fire.
Shropshire Fire and Rescue Service said a crew from Ellesmere was was called to a house near Oswestry on Sunday night and access was “extremely challenging”.