We’ve moved into fantasy territory with this patch (although, all of this could technically have been done in the 60’s. I can’t find any evidence that the BBC had sequencers or drum machines onsite).
This is a more complicated patch, so if you’re a beginner you may have trouble following some of it (just start turning knobs and slider and see what happens). Each row still has it’s own oscillator, but I’ve connected filter cutoff to LFOs.
Oscillators 2,3 and 5 have a NOTE SPREAD slider. This will increase/decrease the range of the notes for each oscillator.

Another super patch, as you say a drum machine maybe pushing it a bit far, would they have made drum loops on tape, or drum tones on tape then mixed them altogether?
I have heard rhythmic ‘drum like’ tracks from the Delia Derbyshire era at the Workshop. So anything was/is possible with a Tape sampler oscillator set up. Look forward to hearing and seeing what you come up with next!
There is still the Wobbulator, and any number of weird effect units created by Dick Mills.
https://webaudio.prototyping.bbc.co.uk/wobbulator/
https://www.youtube.com/watch?v=nXnmSgaeGAI#t=231
A Delia Derbyshire tutorial, alsorts of weirdness on this video. A joy to behold!
Daphne or Delia could probably have made a whole drum kit from a 1 second sample of a rock hitting a tin can!
I’ll check out the Delia documentary. For some reason or another I missed that one.