Do you mean just moving the consumer unit - or the whole shebang
CU/meter/cut-out?

If the whole lot, you will probably have to pay your "wires" company.

EDF charged me £350 for 30 minutes work to move the cut-out 1.5
metres, and my meter company a further £50 to reconnect with a new
meter to the new CU installed by me.

EDF totally ripped me off - and weren't interested when I contested the
price. Nor AIUI is that area covered by the electricity regulators.