Eurostar is advising customers to arrive for the departure time shown on their tickets as normal, warning that they could miss their trains if they arrive any later.

"If you miss your onward connection in the UK or with one of our partners in France, Belgium, the Netherlands or Germany, you can travel on the next available train," the rail operator says in a notice on its website. "Please speak to a member of staff to validate your ticket."

Passengers also been advised to check the Eurostar website or app for the latest updates.

Earlier, Eurostar told passengers in the notice that they could exchange their tickets free of charge if they preferred.

Delays continue to affect trains travelling from Paris to London.

However, delays on services from London to Paris appear to have eased.

According to Eurostar's live departure board, the 5.31pm service from London to Paris has departed on time.

(Image: Eurostar)

The disruption comes as a number of services between Paris and Brussels, and Paris and Amsterdam, scheduled to depart today, tomorrow and Thursday have been cancelled "due to the impact of the exceptional heatwave", according to Eurostar's website.

The rail operator said passengers can exchange their bookings for free or cancel their bookings and claim an e-voucher.

Services cancelled due to heatwave(Image: Eurostar)

Services from Paris Gare du Nord to London St Pancras International have faced disruption since the 9.12am departure this morning, according to live departure boards.

Eurostar said the 9.12am service was delayed because Paris Gare du Nord station was "very busy".

The rail operator attributed delays to the 11.01am service and subsequent departures to the incident at Lille-Europe station.

As things stand, the 6.12pm service from Paris to London, along with later departures, is not showing any delays.

However, the 8.02pm service has been cancelled.

(Image: Eurostar)

Live departure boards show that most of today's Eurostar services from London St Pancras to Paris Gare du Nord have been delayed or cancelled.

The 8.01am service from London to Paris was cancelled, although Eurostar has not provided a reason for the cancellation on its website.

The rail operator attributed the delay to the 9.31am service and those that followed to an incident at Lille-Europe station.

As things stand, services scheduled to depart after 4pm are not showing any delays, although the 7.01pm departure from London has been cancelled.

(Image: Eurostar)

The nature of the incident near Lille-Europe station is not yet clear, local French outlets are reporting.

The railway station in Lille, northern France, is primarily served by Eurostar and France's TGV high-speed rail services.

We will bring you more information as soon as it becomes available.

Eurostar has said in a notice on its website that passengers who would rather rearrange their plans can exchange their ticket free of charge to travel at a different time or date in the same travel class, subject to availability.

The rail operator has urged customers not to come to the station unless they have a valid ticket to travel.

Passengers are advised to check the Eurostar website or app for further updates.