Most trains in the UK have some quantity of allowed bike storage, but there are restrictions which will vary from one TOC (Train Operating Company) to another. If you want to ensure that there will be space for your bike, you will need to make a reservation (and in some cases, this is mandatory). Sometimes you can't make a reservation, such as on local services, and can only keep your fingers crossed.
Ordering train tickets online is well established nowadays, but you cannot specify that you wish to travel with a bike; there is no automated availability checking. It's important to check availability (and make a bike reservation) before you book your journey!
Call Greater Anglia (Abellio) on 0345 600 7245 - option 2. They will arrange reservations on mainline trains; local services will not (usually) be allowed for reservations. For more information, see: How do I reserve a place for my bicycle?.
28 January 2018 (Sunday): Cambridge Cross
11 February 2018 (Sunday): Ely & District CC Hardriders 25-mile time trial