After watching old stuff of him on YouTube, I told my friend with arrogant certainty that it was the banjo he played, not the ukulele. Further research proves us both right: it was a hybrid they called the "banjolele". A rather odd duck, this George Formby, though pretty talented in an old music hall sort of way. His father before him had been a VERY big music hall star, so I suppose it was no surprise. Americans call them "variety acts." George Formby video here.