Unfortunately you are unlikely to be able to grow this plant, as there are no suppliers of live plants or fertile seeds known in the British Isles. Neem can only be grown indoors in this cold climate, and does not fruit well in pots.
Neem will not grow outside in the UK - it needs a heated greenhouse or very warm window sill. Minimum temperature required is around 18°C
From seed. Sow seeds in a pot, cover with 2-3 cm of compost and keep warm inside a sealed plastic bag: germination should take about 3 weeks at 20°C.
Pot on seedlings, once large enough, and move into bigger pots as needed. Neem responds fairly well to being trimmed and can be grown in a 45cm pot for some years in a heated glasshouse. Prune over large plants in spring, and lightly prune again in August if necessary.
Water plants well in the growing season and feed fortnightly using a general liquid feed.
Red spider mite and scale insects can occasionally be a nuisance on long-lived plants indoors.
Some people are allergic to neem, especially to the ripe seeds and mature leaves, so be careful handling this plant. The seeds can cause stomach upsets if accidentally eaten. Large quantities can cause severe sickness. They should be kept out of the reach of children.