Building regulations on vertical chase to the masonry for meter tail installation

Is this from the point of view of the structure: e.g. not too deep; or from the electricians view: e.g. cables buried deep enough to not require mechanical or RCD protection?

Reference should  be made to (c) of the second paragraph of 2.3.1 Cable installation methods of IET Electricia's Guide.

to meet both you may find you need a considerably thicker wall !  You can usually cut up to 33% into a load bearing wall without seriously weakening it and a lot less for horizontal cuts, -but  is it load bearing ? not all are, 
On the other hand the wiring regs assume the hazard is  50mm long screws and nails and require the cable to be deeper than that from the final surface, or the route to be visible, or conduit/trunking etc or to be in a corner.
Mike.

They need to be inside earthed steel trunking set into the wall or covered with earthed steel capping and covered with plaster board with minimal chasing of the wall.

There's no specific legal requirement - the law (building regs) is phrased more in what needs to be achieved (maintain stability etc) rather than the details how to cut a chase. The means of achieving that will vary with the exact circumstances - e.g. type of construction and materials, but the usual rule of thumb (from memory) for solid brick/block walls is 1/3rd the thickness of the brick/block for vertical chases and 1/6th for horizontal ones (so you ignore any plaster/render) - specific circumstances may permit deeper chases though, or require shallower ones. For a cavity wall, you consider each leaf as a separate wall for these purposes.

   - Andy.

Yes, in general with cable installation without compromising structure

It’s the cavity wall I am referring to.

Approved Document A - paragraph 2C30 is probably what you want.

But if you're thinking of taking someone to task over it - keep in mind the overarching condition of all the approved documents: "Thus there is no obligation to adopt any particular solution contained in an Approved Document if you prefer to meet the relevant requirement in some other way."

   - Andy,

Is there any example photo of this kind of installation please?

Its the wall, between external wall and plasterboard . The wall are thermalise breeze block I think.