He is a lodger, contrary to what has been posted on here. As such, he has a right to reasonable notice to leave. Usually reasonable notice would be deemed a week for someone who pays weekly or a month's notice for someone who pays monthly but it's not a fixed rule that must be adhered to in all cases; there could be circumstances where you need someone to leave sooner (or even with no notice), e g because of their unreasonable behaviour; that could range from a threat or danger to you or others or refusing to pay for his lodging or causing you severe difficulties such as disrupting your family life or running up bills you cannot afford to pay or generally refusing to cooperate in any way to the point of disruption and disrespect to you, your children, your house and family generally.
Did you give him notice in writing? The advantage of doing that is that you would have evidence of having given reasonable notice. He can't argue that you didn't give him any notice. You could follow up the notice with a written reminder that he is due to leave on a specific date according to the prior notice and make clear that he will not be allowed to live in the house after that date.
You can advise him to take his belongings with him but if he leaves any behind, legally you have to keep them for a reasonable period to allow him to collect them. After that you could dispose of them.
At the practical level of getting him out you mentioned his having lived previously at the YMCA - since they know him, have you thought of contacting the YMCA, explaining the problems you are having with him and asking if they can help you out by giving him temporary accommodation so that he leaves?
If he refuses to leave, you would be wise to get advice from the CAB, local law centre, Shelter or a solicitor about the legal position and liabilities, before taking action such as locking him out and leaving his belongings outside. If necessary, you could call the police for assistance if he refuses to go and tensions escalate. @