My service provider (Southern Electric) says that their electricity meter can only be moved by a 'Lloyds registered' electrician. Any idea what that means?

Lloyds do operate a scheme called NERS, it stands for National Electricity Registration scheme. As the other reply has said it is primarily for contractors who want to carry out work for the Distribution Network Operators. The DNO owns and maintains the incoming cable to your property that supplies electricity to the meter, without knowing whereabouts in the country you are the DNO maybe another part of Southern Electric or someone else. So if this incoming supply cable is to be altered to allow the meter to be moved then what you have been told is partly correct. If its just moving the meter and not the incoming supply cable, then a registered NICEIC electricain should be able to do the works provided southern electric call to reseal the meter once the work is complete. It all really depends on where the meter is moving from/to and how this affects the cables to your consumer unit and the incoming cable from the road. It may pay you to get a quote from Southern Electric's own electrical contracting company

I believe this relates that contractors that the electricity suppliers - like SSE (called 'DNO's - distribution network operator in the trade) use to work on their own networks. The meter is part of your supplier's equipment and network, so cannot be worked on by an electrician you may employ to work on the installation in your home.