Lodger refuse to vacate

Possession - Section 8 and Section 21

Hi, I am managing a lodging agreement on behalf of a family member. She has a lodger (who signed a lodging agreement) who is staying in an annex connected to the house. He does not share living space other than the garden, which he uses to access his room from the garden side entrance. He has become increasingly difficult to deal with , he is refusing to pay rent, being very confrontational, threatening, does not negotiate, and is refusing to adhere to (he acknowledge receipt) the written notice to quit which we have delivered to him in accordance to the contract. I believe he classify as a lodger with basic protection so we can't change the lock on his door, throw his things out. However, are we allowed to secure the garden access on the premise that the garden is part of the main house that is not part of his lodging, and that he is technically trespassing if he tries to jump over the garden wall to get into his room?