Disclaimier: I am not a legal professional and this is not legal advise just my understanding of the law, I suggest you take professional legal advise if you wish to sell alcohol in the UK.
Really quick answer NO you can not sell your homebrew in the UK.
Home brewing is for personal use only. No one will arrest you if you give out a couple of bottles to your mates to take home, but it is still illegal.
You need to have a license to produce and hold beer, approved by HMRC. Since April 2016 to sell beer as a wholesaler you need to be AWRS registered. Furthermore to sell to the public you have to have a personal license, and the premises from which you are conducting business need to be licensed for off or on trade as appropriate.
From deleted questions/comments:
"section 175 of the licensing act 2003, which allows you to conduct a raffle with alcohol as a prize in some circumstances"
Yes, but this alcohol has to be duty paid you can't just hand out home brew.
"Don't sell alcohol, sell raffle tickets in an “everyone is a winner” scenario"
HMRC got wise to this and clamped down.