"I wonder, is there anyone investigating Dr. Nott for supporting what are likely terrorist factions? Just because our govs do it doesn't mean we can, or can we?"
Of course you can.
The phrase "One mans terrorist is anothers freedom fighter" comes to mind. It can be read as each individual, but it also applies to an entire state.
For example, If Turkey sees the Kurds as terrorists and is bombing them to pieces, then it is fine for citizens of Turkey to support that effort, in any way possible. Those who support the Kurds in Turkey will be labelled terrorists or terrorist sympathisers, and in some cases have already been sent to prison.
However if another country does not see the Kurds as terrorists, then that countries citizens are free to support the Kurds, without fear or arrest or prison.
(However don't go traveling to any countries that do see them as terrorists, as you could be arrested as a terrorist sympathiser under anti terror laws).
Of course, as you can see with the situation with Turkey and NATO, when two opposing opinions on whether a group are terrorists clash between allies, odd things result (like NATO shipping weapons to Kurds, to fight a NATO member, who themselves buy NATO weapons). In that scenario the only people happy are the defense industries.
The UK does not see the "rebels" in Syria as terrorists, so it is perfectly fine and legal for the Dr to support them as much as he likes. Sure, if he went to Syria, he may be in trouble with the law as a terrorist sympathiser, but within the UK it is perfectly fine.
It isn't like Syria is going to declare war on the UK for supporting terrorism or harboring terrorists, and any attempts by Syria to extradite people like the Dr. on anti-terrorism laws would most likely be laughed at.