Believe it or not, you can sometimes take your bike on the tube. The older 'sub-surface' lines (Circle, District, Metropolitan, Hammersmith & City) permit the carriage of bicycles. They're forbidden on other tubes, except for the above-ground stretches at the end of the lines.
In any case, bikes are banned at rush hour (7.30-9.30am and 4-7pm). Folding bikes are permitted throughout the network at all times, but taking one through central London at rush hour won’t make you popular.
Mainline trains all have space for bikes, but there are outright bans or heavy restrictions at rush hour.
On commuter lines, forget about taking a full-size bike at rush hour (usually trains arriving in the city before 10am, and leaving between 4.30pm and 7pm). At other times, you can often stash your bike in a vestibule. Some trains do have dedicated spaces, indicated by a bike symbol on a carriage door.
On long-distance trains, you’re generally required to book a bike space in advance (do this online using the East Coast website), whether off-peak or rush hour. Policy varies from company to company: First Great Western will let you take your bike without booking if there’s space available, but Virgin always insists on booking.
There's one way to get round the restrictions. Folding bikes are exempt from train restrictions, and can be stashed in the luggage rack or discreetly in the vestibule. Today's models are pleasant and easy to ride round town; once you’re used to the twitchy steering, it's only on steep hills that you'll feel the difference from a full-size bike.
Bear in mind that the largest ‘folders’ are too big for luggage racks, and that a cheap unbranded folding bike is almost always a false economy. Expect to pay at least £500 for a good model and often much more, but note that Brompton offer sizeable discounts to London Cycling Campaign members.
Bikes have been banned on the DLR since its inception, but in July 2013, the regulations were changed (for a “trial period”). They’re now allowed outside peak hours, with a maximum of two bikes per set of doors.
There are cycle routes to Heathrow and Gatwick, but they’re both a dismal slog through suburbia. So unless you live nearby, we’d reluctantly advise catching the train.
From the city centre, it'll take you a good few hours to wend through London's suburbs on your way to the countryside. You might be lucky and find a nearby traffic-free route such as the Wandle Trail or the River Lee towpath; more likely, your choice will be between quiet and indirect residential roads, and fast but busy arterials. The Avenue Verte (to Paris) and the London-Brighton run might sound enticing, but the posters never boast about the time you spend negotiating Croydon.
Here’s where the trains come in; the countryside is only as far as your nearest mainline station. An afternoon in Kent? Head to Victoria. The Cotswolds? Just turn up at Paddington. You can even get to the Chilterns by tube (Chesham and Amersham are on the Met).