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.
TL;DR;
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.