Don't mess about: for the difference in cost, go for a 2.5 sq mm cable. You'll end up with less heating effect, less voltage drop and less worry. Standard UK 13A socket outlets are rated ok for 3KW, just don't use two 3KW appliances in the same double socket outlet simultaneously. If worried, replace the socket outlet faceplate you're going to use with a brand new one. Alternatively, get a 16A (blue) "commando" socket outlet installed for the brew machine (E.g.
240V Industrial Range | Industrial Plugs & Connectors | Screwfix.com also available elsewhere).