I have had a further thought about this - Is there a way to get the branch id out of, for example, the crm url and insert it into an analysis code of the relevant order or quote on Sage 200? I can then use the CRM Entity mappings hopefully to map the branch id of the relevant entity in CRM to the relevant analysis code in Sage 200

I discuss similar issues here :

https://community.sagecrm.com/partner_community/f/19/t/13414.aspx

That said, probably the best bet here is to create your own form which inherits from the Sage 200 order form. In CRM you'd have to build your own URL to launch the form (as discussed in the thread I've linked to) to pass the data to the form Constructor as a Dictionary. Then you can override the InitialiseListForm method, pick whatever you want off the IFormArguments object, then repackage the remainder as an implementation of IFormArguments that the base form is expecting and pass it down to the base class. I've done this a couple of times with the Quote forms; the Order forms share the same base class so it should be do-able.