I'm sure there's no reason why you cant have the water meter inside your property, and the lady above you have her own inside her property......where ever the supply enters your home is where the meter is fitted, (where your stop cock is) many houses here in the Yorkshire water region have these meters, and all new ones are also Automated Meters. These are fitted with a built in transmitter that sends the reading to the company when on the road outside your property - this means they no longer have to disturb you to take a reading. I would talk to your supplier about your options
I'm sure other regions are the same as Yorkshire.