I think the only hard and fast rules relate to conifers like leyandii.

Most law rests on what is "reasonable", so be a good neighbour and avoid excessive shading or overhanging, then you should be okay.

Your Rights
You do not usually need to obtain permission to plant a hedge in your garden if it is solely within your property’s boundary. However, you do need to obtain permission from your next door neighbour if you’re considering planting a hedge to separate the adjoining properties right on the boundary line. Provided there are no Boundary Disputes, and if both parties agree to the hedge, you will usually both be responsible for the maintenance of the hedge on your own sides. You can cut the hedge right back to your neighbour’s boundary, although there are some exceptions to this. (See ‘Restrictions’ below).

What are the Restrictions?
If you reside in a particular conservation area or any trees which form part of the hedge are under a tree preservation order, you may need to obtain permission from your local authority to cut back or remove a hedge. Some properties have Legal Covenants which state both the size and the height you can grow a hedge, and any further information will usually be contained in your property deeds. It’s also against the law to trim back or remove any hedges in which birds may be nesting. You should inspect the hedge first before going ahead with any pruning. If you’re still uncertain about this, the best bet is not to cut back a hedge between March and September, just in case.

Your Obligations
Sometimes a hedge can become overgrown and overhang the pavement outside your property. In this instance, your local authority can force you to cut it back or even to remove, it if it’s causing a danger or obstruction to pedestrians on the pavement.

Read more on www.problemneighbours.co.uk

Never heard of any rules about shrub height. There are regulations about hedge heights though, which you can find out from your local authority. Often its 8 feet. But if neighbours are complaining friendly discussion and consideration is usually the best way to go.