As a general rule, houses built after 1920 do have cavity walls and those built before don’t. However, you need to look at the brickwork - if the bricks are all long (whole) ones, then the walls have a cavity in the middle, but if the bricks are both long and short, there’s no cavity because the short ones go through the wall.
Installing cavity wall insulation isn’t a DIY job - it must be done by a registered installer. They’ll make small holes in the external walls, blow insulation material into them and then fill the holes. The installer will need to access all the external walls and if any of the walls adjoin a neighbour’s, they should fit a barrier to contain the insulation.
According to the Energy Saving Trust (www.energysavingtrust.org.uk), cavity wall insulation in England, Scotland and Wales costs around £720 for a detached house, £475 for a semi and £370 for a mid-terraced house, with an annual saving of around £250, £145 and £95 respectively. However, not all cavity walls are suitable - ask a reputable installer for advice.
Insulating solid walls isn’t as straightforward as cavity walls. You can, for example, fit insulated plasterboard inside an exterior wall, or create a new, stud wall along an exterior wall and fill that with insulation. This makes the room slightly smaller and you usually have to remove and then refit or replace the skirting boards, door frames, coving etc, so it’s a lot of work and disruption.
External solid wall insulation is less disruptive because the work is done outside. Insulation is fixed to the exterior walls and covered with special cladding or render (any existing render may have to be removed first). This type of insulation has a number of benefits, including improving soundproofing and weatherproofing, as well as making the inside warmer.