I ripped out the hot water tank about 11 years ago and installed a nice big combi, so that idea is a no go. They actually do a kit so that the immersion is only powered when your producing excess electric, which is a great idea for people with hot water tanks. Battery systems are now available which is a better idea but depends on cost, be great if they still paid 50% when it all went into charging batteries, but I bet they have that sown up!
We actually had an engineer arrive yesterday, around 2pm just to check the voltage, he said it was fine but as the problem only shows up at night he'll recommend a monitor is fitted.