We have a 1950s end-terrance house, with cavity walls currently without insulation. We also have also had a rodent problem since about last November - we don't think they have ever got into any of the rooms but we often hear them in the walls, in the loft or in the void between the ground floor ceiling and upstairs floor. We have had a pest control man in twice, but he has just put poison in the loft and looked for any obvious holes in the outside walls where the mice (or rats?) could be getting in, but says he can't see any. We think the poison has killed several mice (evidenced by the occasional very bad but short-lived smell) but the little blighters keep coming back. We think they may come in from next door - an elderly man lives there, he's very hard of hearing (so probably doesn't hear them!), and has a very overgrown back garden which a local cat takes a great interest in.
Anyway, my question is - would cavity wall insulation help the rodent problem by restricting their movement around the house - or even stopping them getting in? We know they get in the walls and, once there, can get everywhere else very easily. Or would they just eat the stuff?? (I've seen some adverts claiming the insulation is vermin proof - but is that really the case?) Which type of insulation might be best? Polystyrene beads don't sound like they'd help much.
I am aware incidentally that this probably wouldn't in itself be sufficient to stop the mice, but it might help? Also this isn't the only reason why we'd pay out for the insulation - there are also the energy-saving benefits.
Thanks in advance for anyone who can offer any advice here.