Electric Meter Faulty?

The 'new' meter might start at 0 , it might have a figure on it already. The fitter should record this anyway so you'd only pay from that point onwards.

Although its a different "kettle of fish" I had to have my gas meter changed (old dial type) to a dgital one and the replacement had a reading of a few thousand units on it, although the paperwork left showed the fitter had recorded this correctly, along with the 'old' meter reading.

^ That is reasonably important, look at the 'new' meter and if its got a reading on it already ensure the paperwork you're left with has this on it, if you don't have any paperwork left or its not matched up, tell them asap.

The issue I see you're asking is as there's no easy way to 'see' the old meter reading.

Unless someone says otherwise (which is quite likely) logic tells me for the few days its been 'broken' they should average read it for those days...