Rail traffic through the Channel tunnel slowly resumed with more cancellations and delays on Wednesday after an electricity failure stranded thousands of passengers and trapped some for a night in a powerless train.

Two London-Paris trains were cancelled and most trips were delayed in both directions as Eurostar warned of "knock-on impacts" on New Year's Eve.

Christelle Renouf, her husband and two children arrived in Paris from London after a journey that took 12 hours longer than expected.

"After boarding, the train first stopped for an hour because there wasn't enough staff, then it stopped again just before the tunnel, because an overhead line fell" on a carriage, she said in the French capital's Gare du Nord railway station.

They spent the night in a train "without electricity, water or wifi," she added.

A spokeswoman said "an overhead line fell onto a Eurostar train linking London and Paris, near the entrance to the Channel Tunnel."

New Year travellers had to scramble to find alternatives on Tuesday, after the operator postponed all services between London, Paris, Amsterdam and Brussels.

But Eurostar said on Wednesday that services had "resumed today following a power issue in the Channel Tunnel yesterday and some further issues with rail infrastructure overnight."

It added there could be "some delays and possible last-minute cancellations."

One man told local media he boarded the 19:01 train to Paris Tuesday, but at 03:00 am on Wednesday he was still sitting in the train at the entrance to the tunnel.

France's BFMTV reported passengers left waiting into the night on a train from London to Lille without electricity, heating or functioning toilets.

"Nothing electrical is working. It's always the same information – there's a serious problem," a passenger named Herve told the broadcaster from the train, which arrived in Lille early on Wednesday with an 11-hour delay.

As well as the power problem, there was also a failed Le Shuttle train in the Channel tunnel, the 50-kilometre undersea rail link between Folkestone in England and the Calais area in France.

Le Shuttle operates vehicle-carrying trains between Folkestone in southeast England and Calais in northern France.

A record-high 19.5 million passengers travelled on Eurostar last year, up nearly five percent on 2023, driven by demand from visitors to the Olympics and Paralympics in Paris.

Eurostar has held a monopoly on passenger services through the tunnel linking Britain and France since it opened in 1994.

But British entrepreneur Richard Branson – the man behind the Virgin airline – has vowed to launch a rival service.

Italy's Trenitalia also eyes competing with Eurostar on the Paris-London route by 2029.

Tuesday's disruption came as Eurostar faces criticism over its high prices, especially on the Paris-London route.

An electrical fault forced the cancellation of Eurostar services and severe delays on others in August, while cable theft on train tracks in northern France caused problems in June. (AFP)