supernan:
I'm assuming you have a preserved "off-peak" arrangement rather than more recent Economy 7 metering. Its not impossible to switch but there might be meter change costs.
The question is is it worth it.
To compare your energy costs you just need to do a little more work. From your bills find out how much electricity you have consumed in a year for storage heating and everything else and what it costs over the year. Or ask your supplier, they will be happy to help. From your bill find out the unit prices you are currently paying.
Then use a price comparison website. Chose any standard Economy 7 tariff and answer the various questions about usage. You will be given a list of tariffs in price order, the lowest price first. Compare with your own costs and unit prices you obtained earlier.
Job more or less done.