Sometimes yes, depending on what you're pouring and playing. If you're simply gathering in a private hired space, you often don't need anything extra. But the moment you sell alcohol or lay on regulated entertainment, think amplified music, dancing or hot food late at night, on premises that aren't already licensed, the rules kick in.
GOV.UK sets out that a licensable activity on unlicensed premises needs a Temporary Event Notice, served through your local council. Many hire spaces, though, are already set up with the right permissions in place, so ask the host exactly what theirs covers before you plan the bar or build the playlist.
Pro tip: Booking a private space on Peerspace spares you the public-space and street-trading permit runaround you'd face throwing the same event in a park or on the pavement. Message the host to confirm what their licence covers.