I'll start of by saying that I continue to feel very safe living in Abu Dhabi. It is probably one of the best cities in the world for personal safety and security.
Please refer to the latest advice on the UAE on this UK government web page (updated 14th June):
I would stress that "The overall level of advice has not changed."
Keep things into perspective: even in our home countries there is always a threat of terrorism, so we should exercise vigilance.