There are many options here. One basic idea is to install a battery (Tesla seem to be better technology and much better value for money but initial costs are significantly greater) and, optionally, a PV system to charge it off grid.
Why off grid? Because our house has an EPC rating of G for which the current FIT is 0.15p per kWh, around 1% of the cost of purchasing electricity. And the window for qualifying for the FIT closes on 31st March 2019.
This blog gives a back of envelope analysis of the different battery options. Conclusions are that the Powervault 3 7.5kWh option represents the best return on investment, giving back 100% of initial investment within 7 years and nearly 200% within 15 years (assuming 50% of energy is supplied by a PV system and 50% by Eco 7 power from the grid). Clearly, without a PV system it will take longer to reach payback.
There are also options such as TIDE and similar flexible tariffs, which the latest Powerwall (and Powervault?) systems can take advantage of via software (not sure quite how that works). These tariffs however seem to be hard to find for our postcode area. Some phone calls may be needed; and 1st Utility does not seem to offer any Eco 7 or TIDE schemes.
Our energy requirements and historical consumption are clearly relevant, as of today we use twice as much electricity as is provided by a 7.5kWh Powerwall as we use around 13kWh per day; but bear in mind that we can ensure we use as much electricity as possible on an eco scheme so this is still a feasible option.