When creating a costume reflecting the Roaring Twenties, keep these things in mind. The 20s were a time of flappers and jazz music. Although alcohol wasn't forbidden in Britain as it was in the USA, Prohibition-era American fashions influenced British culture. The time period has a definite style element, and you can create that by adding a few touches to a 20s-style suit or coming up with your own period idea.
Find or create your vintage suit. Men in the 20s popularised the zoot suit, which you may be able to find at a costume or vintage store. Alternately, create your own look with a double-breasted suit coat (preferably pinstriped), a black shirt and black trousers. Add a white tie to complete the look.
Slick back your hair with hair gel, and shave your face. Men of the 20s were very clean cut and elegant.
Add some black shoes with spats. Purchase spats or make your own (see the Resources).
Top it off with a fedora hat. Most men of this period accessorised their looks with a gangster-style fedora hat.
Procure a prop gun if you are going to a party dressed as an Al Capone-style gangster.