Operator National Express East Anglia (NXEA) has said trains are running normally on the line to London from Norfolk and Suffolk, thanks to efforts to deal with the wintry weather.
Icicles forming under bridges have been blamed for overhead power lines tripping out on the line.
But patrol teams have been out removing the icicles.
And engineers have been at some of the bigger stations on the line to de-ice trains.
However, First Capital Connect's timetable has been amended for services between London Kings Cross and King's Lynn.
NXEA also said some trains elsewhere in Essex were running to an amended timetable because of the freezing conditions.
East Midlands Trains said its cross country services between Norwich, Ely in Cambridgeshire, the Midlands and the North West were running on time.