UK Property Law
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I would be very happy to help - but unclear of the specific question
Dealing first with your questions (and if I have missed any please advise)
The hedge is their hedge and thus he is wrong to suggest that you need to keep your side tidy. You do not. It is their responsibility. If it trespasses onto your land at any point you can trim or cut it back in any fashion to avoid the trespass.
The fence should be on your land. You do not need to allow them sufficient space to maintain their hedge. You may wish to so as to avoid damage etc. 30 cm would be sufficient.
If the hedge is on your land you can cut it back to the boundary.
I really think that the email from the solicitor is more on instructions than the law. As indicated happy to deal with anything if missed - please rate positive.
By law you do not need to leave them area to trim or maintain the land. The law states that your boundary is your boundary - you do not have to give up 30 cms or anything by law. Equally you can hold them liable for any damage. Happy to discuss further but please rate positive