I have checked the meter daily so I know my electric usage each night is
between 15 and 17 units WITHOUT the storage heater(s) on.
I am charged at 5 p a unit ( kw?)
I put one 3.25 kw capacity storage heater on last night. The electric
meter read 82 units used overnight.

This might be a daft question, then again... I don't think this
applies to you unfortuately :-/

Are you on a pre-payment meter ? - if so, it might be that the rate it
clocks up costs is higher than your true usage (it's a programmable
rate).

AFAIK the dial / display will read the true number of units, but the
maths behind it are skewed for prepayment meters, so you may have (for
the sake of ease of numbers) used 100 units at 5p/unit, but you can be
charged a variable rate over and above the true usage, i.e. you might
be getting charged at a collection rate of 7p/unit - this is often
done for people who have a debt on their account.