Talk

There should be a secure online form on the council website for notifying changes of circumstance. Otherwise write a letter. Tell them why you want to cease your claim and the date it applies from (date DP moves in) plus name address and ref no or NINO.

Change of circumstances form as the previous poster has said, call them or write to them or anything really, they aren't slow to stop benefits it's making them not stop them that's difficult!

I would recommend not doing this until very close to the date you want it to stop though, as they may well stop them immediately even if you've told them very clearly a future date that you want them to stop, and then you have to spend ages trying to sort out getting the last few weeks of HB that you should have had.

Also don't forget that any other benefits you get may be affected by your partner moving in as you will be treated as a couple and your claims have to be joint. Maybe ask Citizen's Advice or similar for advice before you do it just so you know what you're getting into.

I have recently come off HB. I simply wrote a letter stating I no longer wished to claim it and didn't explain further. They simple stopped payment. I didn't send letter till I wanted payment stopping

You may well also lose

Income Support
Single Person Council Tax Benefit
Your child tax credits will change
Your tenancy agreement has to be changed to add him to it