GATEway
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The vehicles in question don't look much like traditional cars. They're strange, boxy, slow-moving shuttles that will cruise around Greenwich.
If you're selected for the trials, which take place between June and August 2016, you will get a chance to ride in the vehicles, as well as take part in interviews and research.
The trials are being run by the GATEway project - an £8 million research project led by the Transport Research Laboratory.
In a statement, business secretary Sajid Javid said: "Making driverless cars a reality is going to revolutionise our roads and travel, making journeys safer, faster, and more environmentally-friendly. Very few countries can match our engineering excellence in the automotive sector or our record on innovative research, and this announcement shows we are already becoming one of the world's leading centres for driverless cars technology."