The basic position is that where he has not contributed to the mortgage repayments, did not contribute to the financing of the purchase of the property or improvement on it and did not pay for a considerably larger share of the household expenses then he will not be able to make a claim on the equity in the property.
Even if he had made some contributions which could conceivably allow him to make a claim the process is very expensive and with no guarantee of success.
He is probably occupying under a form of implied licence at the moment, in order for you to evict him you would have to give him "reasonable notice". The better view is that a month is sufficient for this purpose and particularly where you have made him aware that you wish for him to leave the property. Serve the notice on him in writing, by registered post to your address and state that if he does not leave then you will apply to Court for an order to have him evicted.
If he does not leave then you will have to apply for the order. A solicitor can do this for you or you can attempt to do it yourself (the County Court staff are generally very helpful to lay persons if you give them a telephone call). Chances are that once he realises your serious about a Court application he will vacate.
You are not under a duty to finance his alternative accommodation. Perhaps focus on practical things (eg. locks on doors?) to put in place at home to protect yourself and your son and re-enforce your separation. If he makes threats to you then contact the police. If the threats result in any form of assault then tell the police and ask them to advise you of your right for an injunction against him (he would then not be allowed to stay at the property regardless of notice).
Very difficult situation, you have my sympathies.
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