You can cycle to your heart's content through large capital cities, architecturally interesting towns, World Heritage sites, National Parks, wildlife sites and verdant countryside. Attempt a long distance coast to coast route, or, if you're not quite up to that, there are always shorter route. Follow unused railway tracks, scenic minor roads, forest paths, country lanes and even canal paths. Bristol to Bath is a popular route with one million journeys completed. If you'd like to take your own bike, phone your airline ahead of time to make arrangements.
Most airlines require deflating the tires, turning the handlebars and removing the pedals.
Sometimes there's a small extra baggage fee. Bringing a bike on the Eurostar train to Europe is not a problem, but you must book ahead. Many places in Britain rent bicycles. Tourist Information Centres have lists for their areas. Another option is to book with a bike tour company.