It's totally up to them what model or make they install, but any MUST meet the legal requirements for metering so if it's not broken it should give you the correct result, within the required 1% anyway.
To try and clarify, any load 'draws' both watts and vars but domestically you are only metered on the watts at present. Any meter will count the watt hours, but some additionally count the var hours, this is in effect a totally separate meter in the same box and should in no way affects the watt hour reading. Any display of var hours can be ignored., they simply shouldn't record the number and you shouldn't worry about it, at least not until they start charging for vars in a few years time.
That you believe their meter is faulty and request that they test it, in response they should either just change it or test it on site.
As others have suggested, you could get some sort of meter to do your own test, either a proper electronic watt hour meter or an old mechanical one, but all this will do is reinforce your view as they're very unlikely to take you seriously with a £24 Maplins job. To put it into perspective, I have a proper power analyser on my bench at work and it cost about £8000 (I design control and metering systems for the power generation industry) .
A couple of points though: Are you sure you're not just reacting to the staggering increase in electricity cost over the last few months? Are you sure that both you and they are reading the right numbers?, don't take offence at this, I had the unbelievable situation that a meter reader swapped the day and night readings around. The fact that this meant one had gone DOWN drastically did not phase them, the Muppet just recorded it as an initial reading so the computer stopped complaining !!!
Remember you are dealing with a Muppet on the phone, the very best you can do is persuade them to press the button that says the customer believes he has a faulty meter, any talk of technicalities is completely pointless.
Greg