They coordinate with more or less success over time, most recently through the Active Travel Alliance IIRC, but ultimately they have some different(conflicting at times?) aims and structures that deter merging and often they are effectively competing for the same money, whether member subs, donations or grants.
At least they don't work against each other as often as they used to! (I was thinking of the unedifying public spats between CTC and Sustrans over cycleway-building 25 years ago, but you could go back to BC's predecessors facing off with each other and CTT decades before that!)