Having basic front suspension (swinging arms) but a superior rear suspension (trailing arms) fairly neutralizes the usual 'tail-happy' handling of a rear-engined car.
The problem with cars with the engine behind the compartment is often that of a heavy tail-end, causing oversteer on corners (that is: the heavy tail flies out as you drive round). This was very evident in the VW Beetle with it's swing axle rear suspension, which encouraged the back wheels to tuck in and under as the recalcitrant tail of the thing swung outwards. The Imp's light engine, in conjunction with trailing-arm rear suspension means that this potentially dangerous oversteer characteristic is not present.
The Imp's rear trailing arms were developed by Harry White and a team of chassis engineers.
The handling of the small Hillmans - even in standard form - became legendary.
Quoting from "Apex : The inside story of the Hillman Imp" by David and Peter Henshaw. They interviewed Tim Fry, who demonstrated the Imp to a bloke from Chrysler, just before the take over in 1967:
And the silly American said to me, just as we were coming up to this roundabout, 'Do these things understeer or oversteer?'. And I said, 'Well, I'll show you on this roundabout'.
'You can make it understeer like this, (and we went round the first roundabout), 'or you can make it oversteer like this.' And he was completely silent after that.