I don't understand why you're being told
GWR▸ only compensate for delays that are their own fault. While the CRA may be limited in that way, the rail industry system isn't - it excludes only causes outside the rail industry as a whole.
GWR's passenger charter isn't easy to find (it's not even on the site map - there's a link near the bottom of the full terms and conditions page), but it says the same:
If your journey is delayed because of something outside the control of the rail industry, we don’t normally offer any compensation. This might be things like trespassing, vandalism, someone being hit by a train, severe weather or a security alert.
Note that while the current version is dated November 2018, that text was there in 2015, so should be quite familiar.
You may also like to check in the National Rail Conditions of Travel. There are several links to the PDF on the
NR» site, but
this page provides some extra text about it:
Your Rights
Whilst these National Rail Conditions of Travel set out your rights and any restrictions of those rights, the Train Companies may give you more extensive rights than those set out here. However they may not give you less, unless a Condition specifically allows for this, such as in the case of some types of reduced and discounted fare tickets eg. Advance Tickets. The National Rail Conditions of Travel therefore set out the minimum level of service you are entitled to expect.
It may not offer anything different, but if it does you can pick whichever you prefer.
On that basis, an object placed on the track by trespassers might be excluded, but something left by NR or falling from an embankment or part of their infrastructure cannot. As to tree branches, I can see scope for for wriggling if it's a neighbour's tree, but not if it's NR's - though in the absence of proof it may be hard to get that accepted.