The overhead wire cable came down in the Ladbroke Grove area and left a number of trains without power and passengers had to be evacuated.
Engineers have worked to get two out of the four tracks into London Paddington open for electric trains this morning.
A Network Rail spokesperson said: “We are so sorry for the difficult journeys passengers endured on our railway last night and we will be investigating how and why it happened. The knock-on effects from last night mean operators will not be able to run a full service from Paddington today and passengers should check before they travel. Repairs are ongoing and we hope to have the railway fully open by the weekend.”