I had an exended warranty on my Surface so finally took the trouble to contact the insurers and have it taken away for 'repair'. (I bought a cheap but effective laptop in the meantime to keep us going).
The repair company obtained a new typecover from Microsoft and returned the Surface today. At the moment all is working fine - I've been using it for the last hour. But I'm not holding my breath, and will still never buy a Microsoft computer again.