Nope, that's a goner. I'd say you have an issue with "damping off" caused by pathogens in the soil. I see you are in the UK, so what are your soil temperatures like. Optimum soil temperature for cucumbers is 95 degrees F with the low side being 60 degrees F.
How is the drainage in that pot it's in? Poor soil drainage and excess moisture can lead to damping off and from your picture, I'd say the soil looks very wet.