In a statement tonight, Virgin Trains said:
Despite today's disruption, we are hoping to run a full service tomorrow. We will provide updates in regards to this as we get then.
Anyone who chooses not to travel with us today, will be able to travel tomorrow. Your ticket will be valid on our services.
More top news
In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.