I've just come back from Birkdale on the 15:14, and found on arrival at Southport that if I hadn't already heard about this incident, I would never have suspected it. My train ran into platform 1, and both platforms 2 and 3 were in use and occupied, so I couldn't see the track; but as it was in use, the damage must have been quickly repaired. There were no signs of a fire to be seen - no scorch or smoke marks, and no cracked roof glazing.
It's probably not related, but last Sunday and the Sunday before NR employees were spraying the sleepers on the Northern side of the station with a white liquid, presumably a solvent to remove oil deposits. I didn't see them working on the electric side of the station (wall siding and platforms 1 to 3).
Added on 5.5.21: It's reported in today's (Wednesday)local paper the Champion, that the cause of the fire was that strong winds blew a tree branch on to the live rail on platform 1