I'd have to agree with Howard on this one.
There are too many other differences from New Imperial for it to be a re-engined New Imp.
New Imp didn't have that natty little half loop on the bike stand plus the New Imp top tube above the tank had a longer and more gradual downwards taper to the seat tube.
Also they had a very distinctively lined tank with New Imperial in largish print not script and the print ran right back nearly to the rear end of the cylinder. It is markedly different from what shows on this bike.
Finally, New Imp regularly mounted the hand oil pump either in the tank or on the L/H side of the tank. Not on the R/H side as shown here.
I can well understand a change of engine to customers specification but not all the other changes.
I agree its very similar to New Imp but then again, most of the bikes of the period made up from assembled proprietary components looked similar. That was the fashion.
Whatever it is, Alans family had good taste didn't they!
Cheers, Bob