I have had to analyse business usage and plough through a mountain of gas bills a few times so I am familiar with the calculations but not an expert 
You used 956 units of gas between Sep 20 and the final bill in Jan 21. You use 1328 units of gas between Oct 21 and Mar 22. The monthly average was roughly the same, so I think the readings are correct.
I used the same formula to calculate kWh as Avro used but omitted the volume conversion factor because your meter measures in cubic metres. The volume conversion factor is used to convert imperial gas units (100 cubic feet) to metric gas units (1 cubic metre) if you have an old imperial meter.
This is how I calculated it:
Formula
Meter units 732.40
This is the number of units your meter has counted ie
17487 - 16754 = 733
(I am guessing they had the reading to 2 decimal places, hence the difference of 0.6 units)
I used their figure of 732.40 in my calculations as it is more accurate.
Volume conversion factor 2.83
I omitted this step because your meter is metric
What they did was:
732.40 imperial units x 2.83 = 2072.69 metric units
The next step is:
Metric units x volume correction x caloric value
It should be:
732.4 metric units x 1.02264 x 38.8 = 29060.48 MJ
But they used 2072.69 metric units from the incorrect conversion calculation.
2072.69 metric units x 1.02264 x 38.8 = 82241.09 MJ
The volume correction factor of 1.02264 is to account for gas expanding and contracting at different temperatures/pressures. It is set by government regulations.
The calorific value is how much energy each cubic metre of gas can produce, 38.8 MJ (megajoules) per cubic metre. So this step of the calculation is calculating the amount of energy available from the volume of gas used (which is what the meter measures).
Convert to kwH
You then divide the total by 3.6 to convert MJ to kWh
It shoud be:
29060.48/3.6 = 8072 kWh
Their calculation was:
82241.09/3.6 = 22,845 kWh
This step is just converting one measure of energy (MJ) to a different measure of energy (kWh), like converting inches to centimetres.
Price £/kWh £0.024350
I've then calculated the cost by:
8072 kWh x £0.024350 = £196.55
instead of their calculation of:
22,845 kWh x £0.024350 = £556.26
It's not uncommon for gas companies to charge for the wrong units if records haven't been updated after a meter has been changed:
www.theguardian.com/money/2016/aug/15/gas-meter-blunder-consumers-out-of-pocket-eon-compensation
TLDR: Yes, they continued charging you in cubic feet instead of cubic metres when you changed meter.