I think that's all you can realistically expect. In the same way that highway authorities have standardised approaches to things like speed limits, potholes, road improvements (balancing safety, cost and the efficient use of resources) the railway will have a procedure for tree works (balancing safety, environment, cost etc.).
As you say, a letter like that can't repeat the whole of their management guidance for the subject: there's too much of it. And it's not just about how to do work, but whether, when, and where. The main document I can see is the Lineside Vegetation Management Manual (
NR/L2/OTK/5201). That is public, but is very high level. All the detail is in four modules:
MOD01 Lineside vegetation inspection and risk assessment
MOD02 Lineside vegetation management requirements.
MOD03 Route vegetation management plans
MOD04 Tree Management
Those modules do not appear to be public.