I have a theory on what is happening here.
Us down here in New Zealand, use pretty much the same sort of electrical system that the UK does (with some local variations, of course).
I struck the very same thing you are describing, although it was a while back.
First off, I'm inquisitive to know how this workshop is fed from the "consumer unit", is it fed via a "splitter unit" in the workshop itself or are the socket-outlet and lighting circuits fed individually straight from the consumer unit in the house?
Second question is, how bad is the "dip" when you switch the heater off?, are we talking just a slight dip in lighting level or are we talking "brown-out" territory?
The heater I had the problem with was the same sort of thing as you are describing, it was a 2.4kW fan operated heater, the largest you can supply here on a 10A plug.
What I did at the time, was used what is known here as an interrupted phase tap-on plug, to measure the current drawn by the heater during it running and after it was turned off.
Now you don't need one of these things, if you have a clamp-meter, that will fit into the box behind the socket-outlet that supplies the heater, to test the phase wire current.
What I did find at the time, that at the instant the switch was thrown to turn the heater off, it was like the motor winding was acting like some sort of a choke and creating a "back-EMF" that was upsetting the rest of the electrical system, in the office where it was being used.
Although at the time I wasn't fully convinced that that was the entire cause.
I took the heater home with me, to see if I could replicate the same results, with the 3 phase supply of known quality, I had in my workshop at the time.
Sure enough it did the same thing, although this time I had an oscilloscope on it.
Upon switch off, the current from the heater sagged wildly, into the negative part of the trace, in so much so that I had to change the scale to do the next test.
I don't know that I've helped with explaining this at all, something like this is pretty rare and I'd not seen it since, until you raised the question.
If you are still needing answers, by all means, tap out a post, that's what we are here for.