East Coast website says:
But I can't actually find how to do it. Can anyone shed any light on this?Reserving your cycle
Please be sure to reserve your cycle onto the train of your choice before you travel by:
1. Book online and request a cycle reservation at the same time
When booking via this website, cycle reservations can be requested as part of the booking process.
If a cycle space is not available for your chosen service, this will be flagged and you will be requested to select an alternative service.