My question is quite specific, and I hope it's on topic here because I'm really unsure where to ask it! If it isn't on topic, as well as marking it as such I would ask that you please help me out by suggesting where to ask!
This is a question about UK trains.

Last weekend I took the train from Cambridge to Cheltenham (Spa), via London -- specifically via King's Cross and Paddington. There was a delay on the tube (fire alarm at Baker Street), which meant that I missed my train from Paddington to Cheltenham, and had to get one that got in just over an hour later.

I was under the impression that, because I was delayed by more than 1hr, I was entitled to a full refund of my single ticket. However, GWR weren't interested in paying for the refund, since it wasn't on their train that there was an issue -- and I completely understand and agree with this! However, when I spoke to Customer Service for TfL, I was told that I would be refunded the price of the tube journey -- so about £2.60, or something like that, while the ticket in total cost ~£15.

While GWR, Great Northern, etc operate this "30mins => half refund || 1hr => full refund" policy (with some minor variations between TOCs), do TfL not adhere to this? Should I be able to get the full ~£15 back? If so, I assume it would be from TfL.

On the other hand, since TfL only handle a small part of the journey, if I was say going from Penzance to Aberdeen via London and I was slightly delayed by TfL, but in a way that meant I had to get a train an hour later, it seems unreasonable to expect TfL to fork out some £100+ for the delay...

Any advice would be most appreciated, thanks!

Summary: Tough luck, you probably got as much money back as you could from TfL given the circumstances you've described, as the Tube operates much differently from NR train companies.

TfL London Underground is different from NR franchised Train Companies

While the National Rail (NR) franchised train companies has their own passenger charters, which specifies the level of service customers should expect, and more importantly, the level of compensation a customer can seek, Transport for London (TfL), or more specifically London Underground, is not on the list of Train Companies.

This is further confirmed in the National Rail Conditions of Travel, where London Underground is specifically excluded (page 31):

“Rail Service Provider” means Network Rail, any organisation or person (other than a Train
Company) that operates a station and any person or organisation that hires rolling stock to a
Train Company, but does not include London Underground;

“Train Company” means a company operating passenger railway services which is required
to apply these Conditions to persons purchasing Tickets, under a condition of the passenger
licence granted to the company by the Office of Rail and Road. [...] A list of these train
companies can be found in Appendix A.

For avoidance of doubt, London Underground is not included in Appendix A.
There are some nuances on London Overground and TfL Rail, while being under TfL control, actually being "franchised" train companies, but we will steer clear from that as the OP is likely to have taken neither in this journey.

London Underground gets to say how much they are compensating

As a result, what the OP expected on TOCs, which I quote:

While GWR, Great Northern, etc operate this "30mins => half refund || 1hr => full refund" policy (with some minor variations between TOCs)[...]

... does not really apply. Instead we should look at TfL's condition of carriage (emphasis mine):

8.1.3 If your Tube journey was delayed by 15 minutes or more for reasons within our control, we
will refund you the single pay as you go fare for the journey on which you were delayed. We will
refund the cash value, for the delayed Tube journey, if you bought a paper single or return ticket.
You must apply online within 28 days of the delayed journey.

Notice the use of "Tube journey" instead of a mere "journey" in this clause. This has essentially free TfL from the responsibility in paying out compensation for the rest of your train journey. The term "National Rail" does not feature in the Refunds section (Section 8) of the condition either.

In conclusion, TfL says you are only entitled to compensation for the delay on your tube leg only, but not delay(s) on the subsequent NR leg(s), even it is (they are) a direct consequence of the tube delay.

As an aside, I am quite amazed that Customer Service for TfL actually offered a refund given the circumstances the OP has described. This is not aligned to what TfL say in their condition of carriage:

8.1.4 You can’t get a refund if your journey was delayed as a result of planned service changes
and engineering works or for a reason outside our control, like:

• a security alert

• a customer incident, e.g. a person ill on a train

• adverse weather conditions

which I think a fire alarm could easily qualify.