Hello, my name is Marcus.
Firstly common law does not exist it is a myth.
On the face of it your son's partner has no interest in his home.
Your son can ask her to leave and if she fails to then he can evict her.
She is living there by way of a licence granted by your son that he can revoke. Really just means he has given her permission to live there and as I say he can revoke his permission. I would suggest that if he is minded to do so he should instruct a local solicitor who can formally give her notice to leave and if she fails to go make the appropriate application to the court.
The only defence would be if she was to argue she has an interest in the property despite her name not being on the title.
This is known as a beneficial interest. Is very difficult to demonstrate a beneficial interest.
She would have to demonstrate that there was an intention for having interest in the property. She would have also have to make significant financial contribution and finally demonstrate that she is acting to her detriment.
The latter part is where most people fail in making such claims. The reality is even if she has contributed she has live cheaply. To make a claim she has to demonstrate that she has acted to her detriment. An example for instance if she was not living with your son and making significant financial contribution towards his home then she would have gone and bought her own home. Therefore by remaining in your sons home making significant financial contribution she has lost out by not buying her own house.
From what you say she has not made significant financial contribution sufficient enough to establish a financial interest in the property. If she wasn't living with your son should be living elsewhere and it would no doubt cost her significantly more.
Therefore on the face of it it is unlikely she will have any financial interest in the property and therefore your son has the right to ask her to leave and if she fails he can formerly evict her.