I had a look in "Avro Aircraft since 1900" (or a similar title anyway) which lists the types in back. The note for the Type 678 is simply that it had one Merlin engine and two propellors. Nothing else.
Yes I was right, in the Project Summary in the back of BSP: Fighters & Bombers 1935-1950 there is some very limited data.
Length: 30ft 6in
It mentions no offical specification so I'm presuming it was a private venture. A 3-view is also included but it seems the same as the one on the avroheritge site. I'm not sure where the armament was to go, wing-mounted guns seem unlikely given the two propellers and there is not enough room in the nose.
I missed it there. It's not in the index, and I forgot to check the Project Summary. Oh, dear.
Incidentally, the picture I saw on the Avro Heritage website was a rather nice artist's impression, not the 3-view, so double thanks. But based on that their seems to be room for a gun bay under the pilot's seat - where the cannon go in a Mosquito. Depends exactly where the engine was to be.
Single engined. Planned powerplant was a Rolls-Royce Merlin "mounted in fuselage driving
wing-mounted propellers", no further info available at the moment.
Speculation: given the timeline, it's likely that the intended powerplant was the Merlin I, although it is also possible that it was originally designed with the Merlin E (Merlin I was also known as Merlin F) in mind, although there wasn't that much difference between the two types and the earlier developmental Merlin C. Specs for the Merlin E/F included generating a constant 955 horsepower (712 kW) for 50-100 hours and a maximum rating of 1,045 horsepower (779 kW).
Minor Health Warning: I didn't feel like looking up my books, so I used the Wiki article on the Merlin for a reference, but I think it's accurate enough.
For me it hasn't much of a fighter, although armament could be installed in
the lower fuselage, with the gun barrels or troughs under the pilots seat. But the cockpit
layout seem to be prone to problems with the gunsight, see the similar discussion about
a fighter derivative of the Bugatti racer.
Actually, it reminds me very much on the Miles M.30X, the sub-scale demonstrator for
the Miles X. Of course, it's called a fighter in two sources, but nevertheless I have doubts