The simple answer is almost certainly 'no'. It's possible that there might be a covenant in the deeds of your house (or which affects all properties on an estate), which states that you should keep hedges neat and tidy. In which case, it could be argued that you're responsible for trimming the whole of the hedge.
In general, however, unless there's a specific legal requirement (e.g. because of a 'high hedge' order made by the local council or because a hedge overhangs a public footpath), nobody is ever required to trim any part of a hedge in their garden. i.e. you're perfectly entitled to let your entire garden, including hedges, grow into a complete 'wilderness' unless specific legislation applies. That includes plants and hedges, in your garden, which border neighbouring properties.
Chris