The circuit for the 6V6GT output valve in my Classic TM5 radio is such that the HT goes directly to the screen grid, then to the plate via the output transformer. This results in a plate DC voltage lower than the screen voltage, say 20 to 30 volts.
The data sheet states that the plate voltage should be equal to or higher than the screen voltage, depending on mode of operation.
Any ideas as to why the circuit is as it is??? (I have seen the same circuitry on a couple of old radios).
Any reasons why I shouldn't 'play' with a dropping resistor to the screen??

The 6V6 is not so much mode, but the voltage applied to it. That combination is the most common, with pentodes and not only with 6V6.

Astor & PYE (same factory) quite often ran 6V6's with 315V on the plate. The transformer was also often not shielded and live frame.

Some of these sets have screen dividers. The reason for that is that the screen is not let go below the plate voltage up to a certain point. At 315VDC the screen is reduced to 225VDC.

If you put the set together as per circuit it will work and I see little positive to be gained by changing the screen voltage.

Be well aware that some sets actually change the screen voltage to silence the front end when the set is changed to radiogram.

Marc