The Rutan Ares is actually smaller than the Piaggio Avanti, but these are the only two types of aircraft I can readily think of that fit the description.

Human Alien may I ask firstly, how could you tell that the aircraft you saw was much larger? A low flying Avanti can look pretty large, I've seen quite a few.

Secondly, is it possible that you perceived it as a jet because you wouldn't have expected to see the propellors mounted at the back of the nacelle? A turboprop also sounds like a jet so that may contribute to any confusion.

Edit to add;

It it was, however, plainly very much bigger and quite obviously a jet this is the only possibility I know of, though it's not really got that hammerhead look to it

He most likely saw a beechcraft starship. Although it is not jet powered.