You can vape anywhere in the UK, indoors, legally. This is because:
1) E-cigs do not contain tobacco;
2) E-cigs are not alight
SIMPLES! For those that like the detail, have a look at the Health Act 2006
Electronic Cigarettes – A Beginner’s Guide
OK – I am going to start by making assumptions. Firstly, I am going to assume that you know what an e-cigarette is. If you don’t, have a look around this website. All you want to know is what kind of e-cig will suit you; then...
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The Law
Vaping e-cigarettes is legal in public and indoors. This is simply because nothing is alight, and there is no tobacco and therefore no infringment of the provisions of the Helath Act 2006 - have a look at the legislation here