Fat Tire Bike Tours (sic) are one such company departing daily from just outside Queensway Tube Station for a 4 hour tour of Royal London, which takes in Buckingham Palace, Hyde Park, Kensington Gardens, the Houses of Parliament and Westminster Abbey, as well as other sites of interest.
This is possibly one of London's best and safest areas to cycle as you only rarely have to leave the parks. Even so, the cost of the tour includes an optional helmet and reflective vest to maximise safety.
Tours depart at 11am and tickets are £20, which includes bike hire. For more information, see http://fattirebiketours.com/london