Power factor and domestic electricity billing in the UK?

I think I avoided suggesting that - I was living in his boarding house free while waiting for tenants to leave - and only briefly mentioned the problem to him. But I wondered!

It happened (but not consistently) on several different circuits, so my guess is that there was a possibility of high inrush current if the core had by chance been left partly magnetised when the transformer was last switched off. (Might need to look at B/H curves for the core material in question to be more certain about that but, as others have observed, US transformers - it was military surplus - usually run closer to saturation than ours do.)

Whereas with the capacitor across the input, one would expect a damped sinewave of a fairly low frequency immediately after turn off, as the capacitor and the inductance of the transformer would form a resonant circuit, and that should leave the core pretty thoroughly demagnetised.

Anyway, with the capacitor connected there were no more problems so I stopped theorising!