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Your landlord sounds like an incredible, incredible cunt.
Reading their emails makes me feel a seething rage - I can't imagine what you are feeling.
OK - what does it say in your contract about notice?
Here's some things you should read. And this.
Off the record, you have a reasonably strong position and can make your landlords life quite difficult should they decide to press the nuclear button.
Also, change the locks to spite them.
A landlord can evict you without giving any reason at all in England.