Advice please on getting a “lodger” to move out (UK)?

Is anyone familiar with the process of requiring someone to move out? He’s my partner of 6 years who has been living in my house for 3 years. The house was bought by me 10 years ago and both the property and the mortgage are in my name. He pays me monthly a sum equivalent to half the monthly mortgage and bills. There is no written agreement of any kind.

If I want him to move out what do I need to do, legally? I have bought from the stationers one of those “legal” packs, containing a Notice Requiring Possession for an Assured Shorthold Tenancy (but I don’t think this applies since there was no original agreement). The pack also contains a Notice to Terminate for “lodgers” – I think this is the one I need?

What period of notice do I have (legally or morally) to give him? And would he be entitled (again, either legally or morally) to any payment from me in recognition of his contribution to the house running costs? As far as I can make out, because of the property market the property hasn’t increased in value since he’s lived here, though he has done some decorating and paid for a bit of DIY that have conceivably improved the house.

The reason for asking him to leave is unreasonable behaviour/breakdown of the relationship. He’s been asked verbally to leave on several occasions but has refused.

Final question, if he still fails to leave what can I do about it? Are we looking at a court order, or can I chuck his stuff out and change the locks?