Thanks all so much for your really useful guidance.
I got a specialist round last week to have a good look. I'm not sure we really established what the smell is, but to summarise the appointment it ended with 'I wouldn't light that ever again!'.
I forget all the things she said were wrong with the set up, but a few were:
Hearth too short so burner too close to carpet.
Fibre glass etc falling on top metal plate (blanking plate is it called? where the flue goes through to the loft - made of steel) as not sealed in loft, there's just a big hole - could catch fire.
Hot metal plate touching right up against wood beams.
Electricity cable (I think for outdoor lights) running alongside flue in loft and touching the hot pipe.
Burner too close to side walls - which are made of v thin brick and plasterboard.
Vertical pipe in living room so close to walls it's the wrong type - should be insulated or something.
There were other things that I've forgotten. The summary was it's dangerous, it could catch fire (in the wrong way!) and I shouldn't light it again.
Unfortunately, to replace it with another log burner requires the removal and replacement of bricks (therefore redecoration), new hearth (therefore new carpet!), new chimney flue, etc etc - in other words, a total fortune and a right mess. Unfortunately, the set-up doesn't allow for a gas installation either, without significant upheaval.
So we're going to go for an electric stove - one that looks similar, and stick an artificial flue on it to give the effect. I'm not happy about it, but it's the only realistic solution.
Unfortunately, the installation was carried out by the previous owners. Also unfortunately, as we are in Scotland I have been told that there is no legal requirement for installers to be Hetas registered, so there is no paperwork. I do know who the installers were, but I fear it will be a case of one word against another, and as were weren't the original purchases I'm not sure it's a battle I have the energy to fight. I think we'll have to chalk it up as one of life's hurdles, and just pay for the replacement electric stove.
So, crap news. But I'm glad to know the situation - I could have carried on and persevered with the smell, unaware of the significant risks it poses.
Thanks again for all your efforts!!