Imperial (FT3) gas unit to kwh - unit/s x 2.83 x 1.02264 x calorific value (average figure is 39.5) divide by 3.6 = kwh. Quick version? unit/s x 31.75
Metric (M3) gas unit to kwh - unit/s x 1.02265 x calorific value divide by 3.6 = kwh. Quick version? unit/s x 11.22
Basically, to check they are doing the conversion right, find how many units the bill is charging, and check the actual meter face for whether it says FT3 or M3 and, then multiply the units by the correct calculation above, if it comes to within a handful of units for whats on the bill, then they've charged the correct amount in units.
Also worth watching out for when a meter goes through zero, a lot of systems have issues with this, and end up crediting back from 9995 (imp meter) to 42 on a CV of say 39.1, then charge forward through the clock all the way to 58 but on a CV of say 39.8. You wouldnt think the .7 makes much difference, try it.....
One thing I'll say again, in this life, you and you alone are responsible for your financial position. Nobody else is. People can be held accountable for making mistakes against your financial position, but if you dont do anything to keep on top of things you know you have to pay for etc, then its also your own fault. No business gets things right 100% of the time, whether through fault of systems or staff. So why on earth wouldnt you check your bills/statements/etc each time one comes in to make sure nothing looks wrong? Why wait for something to go wrong, then spend ages trying to get it right?
Oh, the amusing part, the people you speak to very rarely actually fix anything, especially with energy, most of it is passed to a back office to look in to and fix, normally because it wont just involve the supplier, but also their industry partners as well (not competition, but third party companies used to do various jobs such as collect readings, etc). What tends to get things wrong is the systems used to automate...these systems only go wrong because of who programs them......the people who program them tend to be some of the smartest people in the country, not dumb people....so rather than slate companies for being full of dumb people who dont know their bum from the elbow, just consider that stuff goes wrong, and it always will do. The best way to get a good, swift resolution? Be nice and happy when you call and just say you need their help in sorting something out. Call Centre staff bend over backward for people who help in resolving the issue rather than just call up and shout from the off. If things dont work out that way first time around, then just escalate in the same manner, eventually you get the person who has the authority/knowledge to sort it. The shouting part from your side generally doesnt do much most of the time....other than alienate the person you speak to