You need to be very sure your bricks aren't too porous. All bricks absorb water to some extent. Mine are terrible, they're like a sponge. If you live in a windy or wet area or your house is in an exposed position this will exacerbate the water ingress to.
The insulation companies will tell you the glass fibre, polystyrene beads or expanding foam are water proof. They are, unfortunately the whole point is they trap air between them. This allows the water to seep between the individual insulation components. Worse still it can lead to capillary action.
Even if you don't get penetrating damp it is very difficult to make sure the cavity is completely full. If you get voids you'll get cold spots which will lead to condensation on the internal wall which in itself can become a damp problem.
Cavity walls were originally conceived on the west coast of the UK to combat penetrating damp in the wetter parks of the country.
You already have insulation in the cavity air. As long as it is not moving around too much it will insulate to some extent anyway. If it is moving around chances are you have air bricks in which case you want the air to move which cavity insulation will stop.
Lots of people have a had it done with no problems and will claim the house 'feels' warmer. There are lots of others who have had to have walls pulled down to remove faulty insulation.
Personally I'm not entirely convinced cavity insulation saves that much extra heat, there are better ways to save energy, makes sure the loft is prperly insulated, makesure you've got properly fitted functioning quality double glazing. I looked at it and decided I wasn't having it fitted and put another layer of insulation in the attic.
Last point, new homes have insulation installed in the cavity when they are built. This is very diffferent from after build insulation. It should be fitted so there is still at least a 20mm cavity (the panels are held against the inside leaf of the wall) and they have a reflective and waterproof face which faces outwards. Finally you don't get voids.
If you want any more info just Google 'cavity wall insulation diasters'. The photos of walls being ripped down should convince her.