Look, I’ve never been in this position, and I don’t know how I would react if this happened to me, but I’m damn sure that I don’t want to live in a country where people can be chased into the street and beaten by members of the public, no matter what those people have done.
Reasonable force seems to cover it for me. Perhaps there may be circumstances in which it would be reasonable to beat someone to a pulp in the street after chasing them from your home. Perhaps that person kept coming back, and perhaps you found yourself living in a hobbes-like state of nature, or perhaps the police were too busy hassling some Italian art student to come and help you fend off this deranged nutter who kept breaking into your house and threatening your children. There’s quite a few perhapses in there though. If those perhapses came true then ‘reasonable force’ would cover you.
Judges and magistrates are pretty conservative types, if they can’t shoehorn your actions into ‘reasonable force’ then you have probably strayed quite a long way from that which should be sanctioned in a country where the rule of law applies.
Of course if the hang n flog brigade want to live in a place where one is sanctioned to shoot people who come to your door, whether looking for directions or the family silver, then there are many places around the world where you could try.