Pierre Delalande from Eurostar said four trains in and out of England were affected, but that three of those had now reached their destination of London, while one was forced to turn back to the capital.
Trains do not run during the night and a full service is expected to resume this morning.
Mr Delalande said:
Four trains were affected - two from Paris to London, one from Brussels to London and one from London to Paris.
The only one that didn't make it was London to Paris because of a delay after the lightning, so went back to London.
Customers were offered taxis and hotels where necessary, he added.
Eurostar has confirmed that a lightning strike close to the UK entrance of the Eurotunnel has set a building on fire. As standard procedure, Eurostar services have been stopped until the fire is brought under control. Fire services are at the scene, but the flames are not yet under control.
4 trains have been affected by the fire. 1 London to Paris train has turned around and been sent back to London. 2 Paris to London trains and a Brussels to London train are still being held at either end of the tunnel, but are said to be moving "soon". No trains are being held in the tunnel.
5 railway substations are on fire this evening after a lightning strike near Folkestone in Kent. Firefighters are tackling the flames along the line from Dover priory to Sandling station. Hundreds of passengers have faced long delays due to signalling problems since just after rush hour.
The Government will today raise the amount it expects to be invested in infrastructure projects in the UK from £309 billion last year to more than £375 billion.
Almost 300 of the 646 projects and programmes are already under construction.
Chief secretary to the Treasury Danny Alexander is expected to announce:
The building of the UK's first toll road in a decade is to be scrapped. The A14 between Cambridge and Huntingdon will not introduce a fee for use after the improvement scheme, due to start in 2016, is completed.
The railway station at Gatwick Airport will receive £50 million for redevelopment.
A Government guarantee could support finance for the development of a new nuclear power station at Wylfa on Anglesey.
The tube's Northern Line £1 billion extension to Battersea in south west London will be guaranteed.
Improvements to the A50 around Uttoxeter in Staffordshire will start no later than 2015/16.
A £10 million competitive fund to open in early 2014 to test ways to deliver superfast broadband to remote areas of the UK.
The Government is expected to announce plans to sell its 40% stake in the cross-channel Eurostar as part of a target to raise £20 billion through the privatisation of financial and corporate assets by 2020.
Danny Alexander, the chief secretary to the treasury, will announce the Eurostar sale as part of a wider £375 billion investment programme to 2030 and beyond, called the new national infrastructure plan (NIP).
Last month Eurostar revealed it had seen an increase in revenues and passenger numbers compared with last summer.
Sales revenue for the period July-September 2013 reached £207 million - a 10% increase on the same period last year - and passenger numbers in summer 2013 rose 5% to 2.7 million.