Little plastic things weren't in use in the 1920's!
Have a look about two courses up from ground level, you may be able to see a thin, black asphalt-type material just protruding along the top of the bricks.
If you can't see that, are your bricks a deep red colour with a smooth face? If so, they may well be engineering bricks which, because of their density, were used to prevent rising damp prior to the introduction of the asphalt DPC.
You say it's a plain brick wall at the back, do you mean the rest of the house is rendered? If so, are you talking about an extension at the back which may have been built years later incorporating a DPC? In any case, render shouldn't extend right down to ground level because this can allow rising damp to get past a DPC.
Having said all of this, even if you do have a DPC it may well have failed due to the age of the house, in which case you would probably have noticed tell-tale signs such as a damp, foisty smell, peeling wallpaper and a general feeling of dampness where the paper has peeled downstairs, up to a height of about 600mm.
You can buy a dampmeter for around �10 or call out a reputable company to check for you. Hope this helps.