Have you take this issue up with the freeholder?
Is the owner of the downstairs maisonette the owner also of the garden?
Is there a particular reason why he is not allowing this or is he just being awkward?
Under the Access to Neighbouring Land Act the neighbour is required to give you access to his property for any work required to preserve (maintain) your property. That would include painting, check repairing windows, window cleaning, and all usual maintenance matters.
If the owner of the downstairs property steadfastly refuses, I suggest that you get a solicitor to write to him reminding him of his statutory duty and telling him that unless he allows this access, you will apply to court for an injunction to make him give you access and if you have to make the application for the injunction, you will asked the court to award the legal costs against him. If he ignores the solicitor’s letter, you will have no alternative but to make the court application for the injunction.
If he still refuses access, he is in contempt of court and liable to be arrested.
If you think that he is likely to simply ignore any court order, you can ask the court to attach a Penal Notice which is a warning that if he refuses to comply with the order, he will be arrested and jailed and held in contempt.
You would be liable for any damage caused although I am sure that there will be none.
Can I clarify anything for you?
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