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My name is Al and am happy to assist you with your enquiry.
Most break clauses in Assured Shorthold Tennacies stipulate that Notice needs to be served no later than the rent payment date. You therefore need to check the exact wording in your Agreement, but I am afraid it would be normal for it to say it needs to have been received by 1st. If so, the Landlord/Agent is quite entitled to ask you to be responsible for the rent until 1/9.
I am sorry this is not the answer you were looking for. Under law, break clauses need to be complied with exactly as it says in the Agreement, so being only 1 day out in giving Notice renders the Notice invalid.
Can I be of any more assistance to you?