It is possible, and there are a number of research papers demonstrating the possibility that a human influenza A virus could infect a dog (
this one, for example)
However… it is pretty unlikely. Most human influenza strains aren’t capable of mounting a self-replicating infection in dogs, and the concern is more around infection of a dog with canine influenza (very very rare in the U.K., although reportedly more common in the US) and a human strain at the same time, resulting in viral reassortment.
So, not impossible - but very unlikely in practice! Hope that helps!