It is illegal to supply any electrical item in the UK without a proper UK 3-pin plug fitted to it that meets the BS 1363. CE marks on plugs don't mean anything. It must have the BS 1363 kite mark or it's not legal.
Obviously if you got your kit from FastTech or overseas then they don't care about such minor details, but if you got it from a UK vendor write to them and ask them why they are breaking the law.
the problem comes from 2 places. 1 the charger with the 2 prongs is designed to be used on either a European mains voltage, or the US mains voltage. US is 110V and EU is 230V If you put 230V through an item designed for 110V that's not good. If it's a EU power rated charger then this isn't that bad.
The 2nd and biggest problem is the travel adapter
IS NOT FUSED. In the unlikely event of something going wrong there's nothing to cut off the power flow if it all gets too high, and if the adapter
looks like the one on the top left of this page, then it's also possible to touch the metal connecting bits for earth and live while plugging unplugging it. you don't want that. You extra especially don't want that if you have children running about your house.
That said it'll probably work OK, but whatever you do don't leave it charging unattended, ever. (It's good advice to not leave any batteries charging overnight or unattended regardless of how good the charger is.)
The biggest safety risk from e-cigs comes from badly charging batteries starting a house fire. I'd really recommend getting a good quality charger like an XTar or a NiteCore as soon as you can. The largest 4bay NiteCore is about £20 and will last you years, lots of vendors sell them.