I don't know if your proposed position is acceptable. More detail may be needed, but assuming it will be OK you'll need to coordinate three different contractors, Builder (to provide the new meter box), National Grid (I think, to reposition your pipe), then finally your energy supplier (to reconnect your new meter).
It's not a quick process so be prepared for a long drawn out process.
Although usually the new meter is connected the same day as the pipe is repositioned.
First point of call is The National Grid, I believe, ours was at Lakeside House in Northampton.They'll provide a step bt step guide.
It may depend on where you live as to where your National Grid is located.
Costs I had a few years ago was:
Move the pipe 0-2 metres = £454,
2-6 meters = £562,
6-10 meters = £703,
10-15 metres = £857,
15-20 metres = £1028.
These do not include the cost of the new meter box.