The YA/YT and the YB have completely different hand brakes. Whilst the lever between the front seats is identical, the two cables running to the rear brakes work different linkage inside the drums.
It is VITAL that the two cable adjusting nuts on the hand brake lever are fully wound back so there is plenty of free play of the cables BEFORE you adjust the rear brake shoes (see the other brake article on this site).
A car has to have, by law, two independent braking systems. The first is the foot brake that is hydraulic. The second ’emergency’ brake is the hand brake worked by cables. Both use the same brake shoes inside the rear brake drums.
The cables on the YA/YT enter the rear of the back plate and operate a long lever. This lever is pivoted near its top end in such a way that it forces one shoe onto the drum, and at the same time operates another link that forces the other shoe ‘on’, ie, the cable and levers push the shoes apart. This is the standard Morris/Wolseley/MG pre-WW2 system and is also used on the TA, TB and TC. The cables need filling with grease until it oozes out of both ends.
There should be a grease nipple at the cable’s centre. Once the rear brake shoes have been adjusted correctly using the big nuts on the back plate, then, and only then, adjust the cables at the hand brake lever end. If the brakes are stiff, or try to remain ‘on’, the linkage inside the drum may need oil working into the various joints or the cable has ‘unwound’ inside its sheath somewhere; you will need a new cable to cure this.
The YB is totally different and uses the MG TD/Wolseley 4/44 system. The cable is anchored on the rear spring pad and it pulls a lever that is pivoted inside the brake cylinder. Inside this cylinder there are two pistons. The outer one is worked by the hand brake, the inner one by the foot brake. To be able to accommodate lining wear the whole cylinder slides back and forth in the back plate. It is often seized so may need oil working into the slot.
Also, the pistons seize inside the cylinder (see that same brake article on these pages as above for a cure). Again, the cables must be fully wound back BEFORE the shoes are adjusted, and only wound back after correct adjustment of the ‘snail cams’ inside the drum accessed by a hole in the brake’s drum. Fill the cable with grease as on the YA/YT.
The two diagrams should help. Nothing is interchangeable between the two systems.