Where is the engine number?
On 1950s-1960s Audax-body Rootes vehicles (from about Minx Series II), it is on the right side of the engine block (from the driver's perspective), near the front.  You will probably need to wipe some oily dirt off, so you can read the number.

Which model and year is it?
Go this web page –  Chassis Numbers for Rootes Passenger Cars.
The above engine number AB 0383107 has a 2-letter prefix.  Most Rootes vehicles have a single letter prefix.  Rootes Australia stamped an "A" in front of it, to indicate assembly in Australia – except where a Smiths Easidrive transmission was fitted.
The standard prefix letter which follows ("B") indicates that it was made in the 1960s.
The middle part is 7 digits.  In the list mentioned above, a 7-digit number commencing with "B 03" indicates a "Hillman Minx Series V De-Luxe." (In fact I know this engine to have come from an Australian-built Minx Series V).
The suffix letters "HWSO" in the above picture are decoded as follows (see 2/3 of the way down the other page) –
        H = High Compression Engine
        W = C.K.D. Right Hand Drive, Export.
              (C.K.D. = "completely knocked down" i.e. assembled in the destination country)
        S = Saloon
        O = Standard specification

If there's no number stamped into the engine block, it's probably a complete replacement engine from the factory.  The suffix letters only make sense when there's a car body attached to the engine.

The chassis number should be found stamped into an aluminium plaque somewhere under the bonnet.  This one is on a Hillman Gazelle assembled in 1966.  On some other models it might be found at the top of the firewall.

Rootes Australia constructed 2 special models that are slight anomalies –
1. Hillman Minx Australian De Luxe ("ADL"), based on the Singer Gazelle Series IIIC, but having Hillman badges, Minx Series IIIC grille, and Minx Series IIIB De Luxe bumpers.
2. Hillman Gazelle (without a series number), based on the Singer Gazelle Series VI.
These cars bear the engine and chassis numbers of their respective Singer origins.  It is not relevant that the Hillman Gazelle was fitted with the aluminium head engine of the Sunbeam Rapier Series V.  The engine number is in the Singer Gazelle range.