Hello and thank you for your question. I would be happy to assist.
Unfortunately there is no blanket legal rule which is relevant here - your answer will depend almost entirely upon the terms of your lease document. This will set out your responsibilities and obligations and will therefore determine whether or not the consent of the neighbours is required (and whether or not they are entitled to withhold such consent).
Unfortunately, without seeing the lease document, it is therefore not possible to give you specific advice. I would absolutely expect, however, that the consent of the freeholder / landlord will be required, particularly as the works that you describe are structural and, if not carried out properly, could affect the structural integrity of the property. The lease might well specify information (e.g. plans) that you must submit to the tenants and/or landlord in order that your request for consent can be considered. It may require you to pay a certain fee to cover the costs of the landlord in considering your request. Alternatively, it may simply require that you obtain all necessary consents and permits required to lawfully carry out the proposed works, such as planning permission and building regulations approvals.
Where consent is required, the lease may specify that the landlord and/or neighbours must make a decision within a reasonable period and/or may only withhold their consent if it is reasonable to do so. Alternatively, it may leave the matter entirely at their discretion, in which case, you will unfortunately not be able to compel them to consider your request or any supporting information that you put before them.
As such I would recommend that you contact a local property solicitor to review the terms of your title documents in order to advise on the specific obligations they contain. Such an exercise should only take an hour or so of their time and should therefore not be expensive.
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Very briefly, this means that - as expected - the consent of the landlord is required for any material / significant works which would require planning consent. It states that the landlord may not withhold such consent unless it is reasonable to do so in the circumstances.
It isn't relevant, however, to the question of whether the other tenants' consent is required and, if so, whether they are also required to be reasonable or whether they may withhold their consent (and indeed refuse to even consider your request) at their absolute discretion.
It is also important to note that the section that you have quoted is one small part of a much larger document which must be read as a whole in order to properly interpret it. It is usual for such documents to contain interpretation and other provisions which can have significant implications for how specific clauses are read and construed - this is why it is crucial that you ask a local solicitor to review the whole document, rather than small extracts, and advise you on the matter holistically.
I hope that this is helpful and would be grateful if you would confirm by accepting and rating the response below.