If the property is in your sole name and there are no children under 18 who would be made homeless by your actions, then what you have been told by citizens advice is absolutely correct.
If he was a lodger and paying rent, then he would be entitled to one months notice which need not necessarily be in writing as you appreciate, it is better if it is. A simple letter if sufficient.
When the notice expires, you don’t have to go to court, you can simply lock him out provided you give him his belongings back.
However he doesn’t pay rent. She may have contributed by putting in the kitchen or anything like that but he hasn’t paid rent and his financial interest separate from his right of occupation. He has no right of occupation and therefore you could simply lock him out now and give him his belongings back. He has no more right to stay in the property than the post man the milkman, or the man across the road who you invited in for a cup of tea very briefly. The fact that you may have been living together as a couple is irrelevant.
However he may have a financial claim to make against the house. Being named on the council tax bill is really neither here and are there although he could potentially argue that it gives him the right to some notice but it would only be 1 month.
Can I clarify anything else for you?
I am happy to answer any specific points arising from this.
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