Our travel correspondent Simon Calder reports:

Passengers aboard the 7.01pm Eurostar departure on Tuesday evening from London St Pancras International were due to arrive in Paris at 10.19pm local time.

The train left about 90 minutes late and stopped at the mouth of the Channel Tunnel for many hours.

The Independent has tried to establish exactly how late the train is.

The latest information on Eurostar’s travel information site indicates an arrival at 10.19am – 12 hours behind schedule.

Eurostar’s site says: “The updated times show in red are approximate and may change.”

Eurotunnel has issued an updated statement making clear that it was not responsible for the long delay experienced by some Eurostar passengers on Tuesday night, Simon Calder writes.

The company said: “The power supply incident in the Channel tunnel was resolved overnight, and the tunnel has recovered its full capacity since then.

“The overnight incident on the British network is unrelated to this. Rail service in the Channel Tunnel has resumed overnight in both directions.”

Passengers on Tuesday night’s 7.01pm departure from London St Pancras International have been speaking about their gruelling experience.

The train left about 90 minutes late and stopped at the mouth of the Channel Tunnel.

A passenger named Francis Collings told Sky News that the power was turned off around 11pm.

He said: “About four hours ago, maybe about 11pm at night, the power was turned off. So we have lighting, but it's low lighting, but this seems to have affected the toilets, which don't seem to want to flush.”

Six hours after the train stopped, he added: “We’re still here, not entirely sure what's going to happen because there's a fault somewhere, we believe, in the tunnel, but we've also been told it's with the train and there was a fault with a carriage and there's talk of locomotives pulling other trains that are further up the line out of the way.”

Tens of thousands of passengers who were expecting to travel on Eurostar yesterday are waking up on New Year’s Eve where they did not expect to be, Simon Calder writes.

Thirty trains linking London with Paris, Brussels and Amsterdam were cancelled on Tuesday 30 December.

Passengers have been told to rebook, but it appears that many have simply abandoned their New Year journeys.

Problems began in the early hours of Tuesday morning with a power failure in one of the tunnel bores between Folkestone and Calais. There is a well-rehearsed response to this, which is single line working: a sequence of services, comprising LeShuttle car-carrying trains, freight trains and Eurostar passenger services, travels in one direction.

When they are all through, trains travel in the opposite direction. It slows everything up, but people and goods get through eventually.

But then a LeShuttle train broke down, and everything seized up.

Initially Eurostar dispatched trains towards the Channel Tunnel hoping the blockage would be removed. But by late morning the train company was sending them back to where they started, and urged passengers not to try to travel.

Trains resumed around 4pm, but by that time many people had given up.

Services have now resumed, but passengers have been told that unless they have a confirmed reservation for one of the trains that are running, they should leave the station.

Eurostar passengers have been cautioned that further delays and cancellations remain a possibility, even as services have largely resumed following a significant power outage within the Channel Tunnel.

The cancellation was attributed to a dual issue: an overhead power supply problem combined with a failed LeShuttle train, which together blocked all routes.

A statement on the Eurostar website said: "We plan to run all of our services today, however due to knock-on impacts there may still be some delays and possible last-minute cancellations."

The first train of the day from London St Pancras to Paris was cancelled and the second was delayed by nearly half an hour.

Others appear to be scheduled as normal, although a new statement from the operator says that “due to knock-on impacts there may still be some delays and possible last-minute cancellations”.

Eurostar passengers have been warned to expect disruption today despite the resumption of services after a power outage in the Channel Tunnel.

Thousands of passengers faced hours of delays after the train operator cancelled all its London to Europe services on Tuesday when an overhead power supply problem and a failed LeShuttle train blocked all routes.

Some services resumed on the single available line on Tuesday evening with Eurostar saying there were “further issues with rail infrastructure overnight”.