The first question you should ask yourself, before thinking about wall insulation, is 'what type of wall have I got?'
Solid walls were built up until the 1930s in most parts of the UK. By 'solid', it means that there is no cavity inside them. A solid wall's brick pattern is recognisable by having lots of end bricks, which look like half-length bricks, in the middle of walls (i.e. not near ends of walls and not near windows and doors). These are in fact mainly cross bricks, which run from the front to the back of a wall. Therefore the depth of a wall - ignoring any plaster on the interior surface - is a brick's length, about nine niches.
Cavity walls consist of an inner leaf an outer leaf, and a gap in between. Ties, which depending on the era are made of metal or plastic, hold what is effectively two walls together. The brick pattern shows many more full length bricks. Obviously the depth of the wall is greater, as most cavities measure at least two inches.
There are some other types of construction, such as timber frame and no fines, but these are comparatively rare. 'No fines' homes were more often built by local authorities in the 1940s and 1950s for council housing, and can be treated as solid wall for insulation purposes, although (uninsulated) they perform a lot better than older solid wall properties.
Cavity walls lose less heat than solid walls, and are much easier to insulate.
Some parts of the country are fortunate in having relatively old homes with cavity walls e.g. North East England. Unfortunately for the East Midlands, solid wall construction continued into the 1950s.
Obviously the more external walls you have, the more heat loss you will experience. So a detached house loses more heat than a mid-terrace one, for instance. Also, some old homes with solid external walls may have extensions built with cavity walls.
It is not unusual for people to investigate getting cavity wall insulation when they already have it installed.
Homes built in the last couple of decades are likely to have had insulation put in the cavities when they were built. Otherwise, you may be able to tell if you've already got cavity wall insulation by looking through the papers handed over to you when you bought your home. Cavity wall insulation often has a 20-25 year guarantee. If you live in a low level block of flats, insulation installed by the owner of a flat above or below will also have insulated your property, as the cavity needs to fill from the bottom upwards.
Physically you can check whether you have cavity wall insulation by looking for drill holes, at about waist height, between bricks, at about one metre or one metre and a half intervals, all around the outside of your home. These will have been refilled with mortar (cement) but may show up as a slightly different colour. Another check is to go into your loft and see if you can take a look at the tops of the walls. It's not always possible but sometimes you can see them, and it is likely that some insulation will have spilled out of an open cavity.