Thanks to everyone who replied. I found my way around the Iberdrola website with all your help and have now signed up for the '8 hours a day' tariff.
I did this because of the heavy use electrical equipment we have (hot water boiler, swimming pool pump, dishwasher, washing machine, etc) and the way we use it. It made more sense to sign up to this tariff than to go for the night tariff.
With the 8 hours tariff, you can select your hours through the day and break it up into blocks that suit your usage, so we've gone for 0800 to 1200 and 1600 to 2000 each day. The cheap rate on this tariff is slightly more than the cheap night rate on offer, but not much. It is saving about 35% on my previous tariff during the cheap 8 hours, but this is counterbalanced by it being 28% more expensive in the other 16 hours. Since we use most electricity in the 8 hours, it SHOULD work out cheaper overall!
I'll wait and see.