bad tenants

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New elderly landlord! Allowed tenants to move in furniture July 2011, so gave them key. They moved in whole family, paid part deposit in cash, but refused to sign a tenancy agreement. No payments been made and no tenancy agrements signed.
They have contacted local housing to get two properties one for daughter and child, one for parents and child. Think using me to be made homeless so council will have to house them - but actually making themselves deliberately homeless.
Man big bullying vindictive so I am keeping well away.
Should I sue through small claims court, but think this is only up to £5,000, not enough to cover back rent. What notices should I send them? Not been allowed in to check property. Do not allow dogs but two young dogs in property and have destroyed garden and lawns.