Have you got an actual reading for the day your partner moved in ? If so then the amount used in total will be the actual reading now less the actual reading when they moved in. You'll then need to make sure that the total usage on the estimated bills is the same as the actuals and check that any apportionments re price rises look reasonable. That will gve you the total amount due for the period of occupation and taking any amounts actually paid off that will reveal the true amount due.
If your partner didn't get the meter read when they moved in and all you've got is an estimate as a starting point then I suspect that is all that can be used so you're stuck with it.
I know it's not strictly your legal responsibility to read the meter when you get an estimated bill but it is the only way to make sure you are being billed for the correct usage. If that means ringing the maintenance company up 10 times until they get so fed up with you that they come and do it then that is what it takes. It's your money and your account that get messed up if the meter readings aren't reported regularly.