The insect popularly called "a wasp" in the UK is European paper wasp. This is certainly not the same as the Yellowjacket, the American popular name for various species of Vespula and Dolichovespula, which are more closely related to the hornet family than UK wasps.
The "conventional" way to eradicate UK wasps is to destroy and/or poison the nest, with DIY products such as these: DIY Wasp Control Products or for a large nest, by hiring a pest control professional who will have suitable protective clothing to avoid a massed attack.
The UK wasp species builds a new nest each year, and are unlikely to attack humans unless provoked. Unless they are causing an identifiable hazard (e.g. to pets or young children) they can usually be left alone, in the knowledge that they won't be back next year. The behaviour of hornets is less people-friendly, of course.
The most dangerous time for UK wasps in autumn - they feed on the sugar from rotting fruit, and tend to pick a fight with anything when they get drunk if the fruit was fermenting (just like some humans...).