I wonder if there's any chance of finding out what happened here?
My electricity bill is £350. I pay be direct debit and the balance
floats between £300 and £350. Thing is, about 3 years ago it floated
between £70-£100.
I do remember at around that time the electricity meter was changed

There are several places where this could have gone "wrong" - indeed the
bills may now be accurate and under-reading before, but...

Your property will have an MPAN (meter point administration no.), and
your supplier will nominate a meter operator (who may or may not be from
the same company)

Given the number of companies and computer interfaces involved in
transferring this data to anyone who needs it, it is not unknown for the
old _or_ new meter reading to have been taken down incorrectly and then
tacked to the wrong MPAN number...

As a suggestion:

a) check the meter serial number corresponds to the one on the bill

b) see if you can get the meter readings at the time they were changed -
you may need to make a guesstimate at your usage using prior bills to
get an approximate final reading of the old meter if you have no actual
readings available

c) check in the vicinity of the meter - there may be a sticker to say
what the readings were when it was changed

d) if your supplier doesn't provide any useful information in a
reasonable timescale, contact http://www.energywatch.org.uk