Given the reported time elapsed after takeoff and altitude when passengers noticed problems, it makes a birdstrike far less likely because at this time of year geese (it would need to be that size to create the kind of problems) are v unlikely to be moving about at the height and in the formation needed to damage both engines. It is just possible, but if so it's really a very freak event.
If media reports from passengers are correct more concerning is if port engine was shut down and starboard was alight, it's a wonder they got back to R27 at all. I'm glad I don't live in Hounslow.