UK Property Law
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Thanks for your question.
Yes, she can. She can sue you via www.moneyclaim.gov.uk for the rent you owe under the contract. I'm afraid that it does not matter that you did not actually sign the contract, by occupying the property you have impliedly contracted with her.There may be onerous terms in the contract which she would have difficulty enforcing, but rent is not one of them.
Your best way forward (if you think she'll actually issue a claim if you don't pay) is to acknowledge the debt but say that your a bit short at the moment and offer her a repayment plan by paying what you can not with more to follow incrementally later.
Sorry it could not be better news.
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