For clarification of some of what has gone before . . .
Under both the Health Act 2006 (which applies only in England and Wales) and the The Smoking (Northern Ireland) Order 2006 smoking is illegal in any enclosed space that is "open to the public" and/or where "the premises are used as a place of work by more than one person (even if the persons who work there do so at different times, or only intermittently)".
"Smoking" is defined as "smoking tobacco or anything which contains tobacco, or smoking any other substance".
However neither of those Acts (nor the equivalent legislation in Scotland) applies to using products which aren't actually "lit".
So vaping isn't illegal anywhere except when separate legislation applies (as it does on UK railways).
However most shops, bars and restaurants (etc) place their own bans on vaping on their premises, as do many employers.