There are no laws preventing or restricting where you can use e-cigarettes. Some places, such as some sports stadiums and most airports, do not allow vaping while others do. If there are no signs indicating this then you should always ask. But it helps to be respectful when using e-cigarettes around others, especially non-smokers.
thrNow wants to note that the above answer applies to the United Kingdom. We hope one day Australia will adopt this sensible outlook. In Australia, while we push for our laws to catch up, the best way to avoid any trouble is to only vape in places where smoking is allowed.