I suppose you could turn off the boiler and see how many units it takes the hob to bring a known quantity of water of known starting temperature to the boil. Then you could either perform a calculation based on some assumptions about efficiency or you could compare with the identical experiment at your own house, trying to keep the flame size the same and using the same saucepan. Obviously a very large quantity of water will give you a more reliable indication but I wouldn't bet on this being very informative.
The other thing it might be worth doing is turning off the boiler and just seeing whether the meter moves of its own accord (and calling SGN if it does).
Faulty meters UNDER read, usually.
Are you comparing units used, not just the bills?
The hob relies too much on the efficiency of the burner to heat water.
For electric the only thing I can think of to use is a kettle, unless there's an immersion heater for water?. Look on the rating sticker , it'll say 2.4kW or 3kW or similar. They're usually a bit less than it says.
Turn big loads like washing machine off.
Kettle off, take an accurate meter reading, wait 3 minutes, take another one. It shouln't have moved much with just lights etc.
Fill the kettle, take a reading, lettehe kettle boil 3 minutes, take a reading. Leave the kettle lid open in case it boils then it won't turn off.
If it's a 3kW kettle like mine, the leccy difference when you had the kettle on should be
3kW x 3/60 = 150 Watt-hours. See how that compares with the meter reading difference.
At 28p per unit that'll be 4.2 pence worth of power.
Gas is harder.
Does she have a combi boiler or...??
Same principle, you have to get it running flat out for a timed period of a minute or two, and take two readings.
Then you have to assume you know what the usage of the boiler is, and it hasn't turned itself down in your minute or two. You'll have a result in cubic feet for an imperial meter, or cu metres for a metric one. Some of the later meters are dogs to read at all, you may need to google that.
Then it's a simple sum to convert to kW, which should match what you know about the boiler, but it won't be very
accurate because meter accuracy could be out, and it'll depend how the boiler's set.
1092/cu ft in 1 minute gives you kW, or 321 x cu m in 2 mins gives you kW. Iirc.