There’s no British High Commission in Swaziland. If you need emergency consular assistance you should contact the British High Commission in Pretoria.
Most visits are trouble-free. Crime levels are relatively low for the southern Africa region, but you should take sensible precautions. See Crime
You should avoid rallies, demonstrations and gatherings as these can be dispersed forcefully by the police.
There is a low threat from terrorism. See Terrorism
Take out comprehensive travel and medical insurance before you travel.