Quicker trains would run on a  new rail link between Old Oak Common and the West Coast Main Line.

Passengers would also no longer have to change at Euston making it easier to get on with the job of rebuilding the station so it matches the standard of Kings Cross and St Pancras.

Transport Secretary Patrick McLoughlin confirmed a study into the extension during a visit to Farringdon station on Thursday where he met with the 100th apprentice appointed by Crossrail contractor Bam Ferrovial Kier.

McLoughlin said: “We are investing record amounts to build a world-class railway, so it is vital we seize every opportunity to make the most of these once in a generation schemes.

“That is why I have asked HS2 Limited to work closely with the Crossrail sponsors to look at extending Crossrail services to key destinations in Hertfordshire.

“Not only would this be a huge boost to passengers and the local economy, it would also provide flexibility when building HS2 into Euston, making sure we create a lasting legacy for the station.”