Thank you very much Chris and Mike. So, two things; 

1. How do you predict the attacking frequency?

2. If the concept is enhanced by reducing the mesh size (I think that is what Mike suggested), could the rebar of a poured concrete slab be used or is ferromagnetic material out?

Thank you very much Chris and Mike. So, two things; 

1. How do you predict the attacking frequency?

2. If the concept is enhanced by reducing the mesh size (I think that is what Mike suggested), could the rebar of a poured concrete slab be used or is ferromagnetic material out?

1. How do you predict the attacking frequency?

Know your enemies, try and capture a sample of their equipment. Or place a guess that it will be short wave or higher, as to radiate lower freqs / longer wavelengths needs massive antennas - either deliberate ones, or accidental ones. Many buildings and bits of kit have wires metres long that act as accidental antennas in the VHF, some buildings have wires tens of metres long that act as accidental short wave antennas, and very few have  wires hundreds of metres in extent that would radiate well on medium wave.

EMC standards reflect this fact, (which relates to the fact the humans are meter scale animals and therefore usually build on a scale that is fractions of a metre to tens of metres,) and require radiated tests from 30MHz upwards (10m waves and shorter) , but assume that anything slower (longer waves) is likely to be conducted up a wire and amenable to filters.

The saving grace at the other end is that higher frequencies are harder to generate by accident, so are less likely to be flying about, and generally accidental radiators  roll off above a GHz leaving you with intentional radiators like only comms systems and RADAR kit to think about  (maybe the odd leaky microwave oven on 2.4GHz) and normally you know where they are.

2. If the concept is enhanced by reducing the mesh size (I think that is what Mike suggested), could the rebar of a poured concrete slab be used or is ferromagnetic material out?

And yes rebar weld mesh of half inch steels on 6 inch centres is very good as a screen for freqs up to about 100MHz, so long as you can weld onto the edges and or bend it about to make the box continuous.
Chicken wire is good up to UHF (say about 500MHz),again the problems are the joints.~ finer meshes are sometimes used as a material for the reflector dishes for field deployed parabolic dishes - as well as being easier to carry to site they are better in the wind as well.

The facility we have at work for our high energy pulse power tests has copper mesh observation windows of 1.5mm weave pitch, that do start to  leak a bit by you reach 10GHz (3cm) but if you are silly enough to get in and shut the door, no mobile phone or walkie talkie signals will get in or out. (GSM handset signals ~ F= 900MHz wavelength about 1ft some of the newer 3/4gStuff goes  up to 2.1 GHz waves of 15cm or so) 
If you ever have to design something like a nuclear bunker you end up with mesh in the air ducts and that sort of thing, and every where else fully welded steel floor, wall and ceiling panels, and spring seals on the doors.
If it really needs the ultimate and you need a decent flow of air or water so a solid panel with some pinholes will  not do, then honeycomb  welded panel, is the way forwards and electrically looks like an array of tubes, any one of which is too small to permit significant radio wave propagation. In this case they start to leak when the radio half wavelength approaches or is less than the guide largest interior dimension, and they begin to behave like waveguides

M