Outside peak hours they are allowed on the sub-surface lines (Circle etc) as those have larger trains and simpler emergency evacuation.

It's still not something you'd want to do very often. I think I did it once with a new bicycle that I'd bought from the other side of London, where the route home would have been long and completely new to me.

Map of allowed lines: https://content.tfl.gov.uk/cycles-on-public-transport.pdf