I used to plan in domestic gas supplies/moving meters for Transco. But I think Transco got replaced by the National grid. Info here
Although the work was contracted out, only Transco could authorize moving of a meter.
About 10 years ago I think it was around £140ish to move a meter. Often its a nice and straight forward job used to give an engineer (used on the loosest terms, defo not the brightest spark, no pun intended) about 3-4 meter moves a day. Though if pipework needs to be replaced then it can take a bit longer, especially if they need to dig in the road.
We used to have a rough lead time of about 3 weeks once payment was received, though if pipework was needing to be replaced the job would have to be scheduled in again.
If I remember correctly, changing suppliers didn't matter as the meter were the same. I think we only replaced old meters for new as and when required.
Hope it helps