Apple trees will need a pollination partner. That is, another apple (or crab) nearby. Do your neighbours have apples,
Saffy? You can grow apples in very small spaces...either by growing them as a cordon, or training an apple to grow in 2 dimensions on a wall or fence, or even something called a 'stepover'. My point being, you will need 2 different trees, but both within the same pollination group, in order for the fruit to be pollinated and develop into apples.
Fruit trees which are self-fertile (which grow without needing a different pollination partner) are cherries, plums, nectarines, gages, damsons and apricots. Pear will also need another pollination partner (and in some cases (Comice pears, Bramley apples), 2 other partners are needed because the parent plants are triploid and must be pollinated by 2 other pear varieties.
You will also need to consider what sort of size you want. This is controlled by grafting the apple (scion) onto vigorous one year old plants (stock) which determine the eventual size and vigour of your chosen tree.
Many fruit trees and some ornamentals are grafted onto rootstocks. These rootstocks control the vigour of the plant, allowing the cultivation of trees and bushes in a smaller space than if they were grown on their own roots.
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An apple will give you a lifetime of joy. Fruit to eat, blossom for our spring pollinators, autumn colour and a beautiful architectural branching sculpture over winter. It is an investment of time, energy and love and will repay you a hundred-fold. It is worth choosing carefully and buying a plant from a proper tree nursery such as Frank P Matthews, which will be lifted from the ground as dormant bare-roots (usually maiden whips (1 year old) or 2 year olds which have already been selected for training. When you have decided what size and shape you want, there will be lists of local fruits which will do well in your soil and climate. There are thousands to choose from but fortunately, the choices can be marrowed down so that you end up with the best plant for you and your garden.
No need to rush. The bare-root season stretches until spring...although it is always better to plant early to take advantage of the last summer warmth in the soil and encourage establishment during winter rains, so always best planted before Xmas.