London Midland, Southern and Virgin trains are being affected by the delays, which are expected to last until midday.
Passengers are being advised by National Rail that services may be delayed by 50 minutes, cancelled or revised.
The National Rail have informed passengers of the delays on the website: “The overhead electric wires have been damaged near Leighton Buzzard. One of the four lines remains blocked which means trains will have to pass the affected area at a reduced speed.
“Some congestion, train crew and stock displacement in the area may mean that trains will continue to be delayed until this line has reopened.
“We anticipate a good service will be operating by approximately 12:00.”
London Midland customers are being advised that their tickets may be used on East Midlands Trains and Thameslink between Bedford and London St Pancras International, Chiltern Railways between Birmingham Moor Street and London Marylebone and Virgin Trains on all reasonable routes.