He shouldn't be entitled to any part of the increase in value from the date he left up to now, assuming he has paid nothing towards the house in that time.
What he is entitled to for any increase in value during the period he was living with you probably depends on what contribution he made to the costs during that time. I don't think it would necessarily be 50% - for example if he was paying all the costs he could probably argue for quite a bit more. You may well need valuations as at the date he came to live with you and the date he left (you will probably have to pay an agent to do these), and a reasonably accurate indication of how you split the costs during that period.
Probably best to see a solicitor who specialises in family law for detailed advice.