Owain, Try this before you get the spanners out. With the bike on its stand, rear wheel off the ground, apply the brake and try to rotate the rear wheel back and forth. Any movement between the drum and hub is down to wear on the drive flange,which is bolted to the drum,and the hub splines. Worn splines or a loose drive flange will give a clunk on load and over run, and on braking. Anything that allows the shoes to move while in contact with the drum will also give a clunk. See if the brake backplate moves. The backplate needs to be moved back to tension the chain and loosely tightened against the suspension lug with the big nut before finally aligning the wheel in the frame and tightening. The spindle nut can then be tightened.. In other words the backplate is tightened against the lug after final wheel and chain adjustment and does not float once all is assembled.
The brake is straightforward to check, first establish that the nut securing the fixed shoe pivot is tight. Loose could be the clunk.The fixed shoe pivot sits in an elongated hole, so with the retaining nut loose, the shoes can move slightly. Apply the brake to centre the shoes and retighten the nut with the brake held on. A few other things to note. Cam pivot wears, sometimes a custom bush will reclaim an otherwise good backplate. Cam lever position and splined pedal shaft will allow adjustment so the shoes just kiss the drum and neither lever passes the magic 90 degrees between lever and brake rod. A brake pedal that rises and falls on light braking means an oval drum.
Swarfy.