Requests for information about fast growing evergreen shrubs is a regular question to the Sunday Gardener. We all like privacy in our gardens, and sometimes there is a need to create a hedge or buffer quickly, but still avoiding the blandness of conifers and problems of Leylandii. Whilst it is not illegal to plant Leylandii, your neighbours can complain to the council if the trees or hedge you plant breaches the The Anti-Social Behaviour Act (2003)
In essence this law applies to hedges of consisting of two or more evergreens, or mostly evergreen trees, (not to individual trees) and hedges over two metres affecting domestic property. This means is that if you pick a shrub which is very fast growing you will need to be scrupulous with maintenance and pruning so as not to offend neighbours and the law. If in doubt, you should take legal advice from an appropriate source such as Citizens Advice or a solicitor.
If you are planning a hedge or screen in proximity to your neighbours, you need to be aware of the law and act sensitively. As an alternative you could consider planting a deciduous hedge, such as a Fagus, the common Beech which is fast growing and not evergreen. It give privacy but a less dense shrub creating less shade.
Planting a fast growing shrub is good in some ways as it produces a more instant result, but a fast growing hedge produces a lot of growth quickly and needs regular pruning. It can also produce very dense shade around it. It is important to view the space and surroundings before making a decision. For example, Portuguese laurel is correctly billed as a fast growing evergreen, but it also gets very large quickly and in around 7 years can reach 7m and 2/3m wide which if planted on a boundary could swamp the area and be unmanageable.
It is a question of balance, to cover or clothe a fence or unattractive spot in the garden weighed against the size the evergreen will become and how quickly. It is great to get the cover, but you do not want to have to spend time, or money cutting back to prevent the evergreen taking over. With that caveat there are a good number of easy, fast growing evergreen shrubs.