You cannot travel to the UK with just a Schengen. The UK is not a part of the Schengen and will soon not be a part of the EU as well. As a result, they have an independent visa regime. If you want to enter the UK, you will need a UK visa.
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What are the benefits of Schengen? The Schengen area allows more than 400 million people to travel freely between member countries without going through border controls.
Bulgaria, Croatia, Cyprus, Ireland, Romania and the United Kingdom are EU states that are not, or not yet, part of the Schengen area. This means that a flight from one of these states to a Schengen state is regarded as an external flight and is subject to border checks.
Schengen started in 1985 with just six countries. The UK opted out of the initiative, having much less interest in scrapping border controls because of its island geography.