You might be entitled to compensation due to the strike days if you had specific plans and can for instance provide evidence of booked domestic flights/coach rides.

I'm however surprised: you indicate you live in the UK in your profile, so as such should have opted for an Interrail pass. That would only have allowed you to use two travel days in the UK. Please do not abuse these passes to travel cheaply within the UK, as there is little necessary for UK railway companies to stop accepting them.

You are only able to use 2 of your total days for travel in your home country so if you had already used them then there would not be any further validity for use in or from UK. You would have had to pay for additional travel in any case.

If you feel you were prevented from using the pass fully then you can always request an extension of validity to use the remaining days, I have no idea if interrail customer services would entertain such a request though.

Edit: Didn’t see you mentioned Eurail. Your profile says UK, this would need clarifying first.

I am a UK citizen but living in Hong Kong for over 10 years (with ID / residence docs as required) so can (in fact, should) use Eurail. Just to stop worries about abusing!

I was planning to use this ticket with a flight into and out of Europe, and train to/around UK in the middle. I would have used the ticket for 4/5 trips in UK, and will end the pass likely with 4 unused days. 

Extending is not really much use (as I will leave Europe), but perhaps if there is a way to claim compensation. The obvious thing would be to “downgrade” to another ticket option but I doubt this is allowed even in this situation. 

You should claim delay compensation for all journeys that you couldn't make. Delays are split in different categories, where you get a lower compensation for a 60-119 minutes delay and a higher compensation for a delay of 120 minutes and more. A cancelled train is a delay of more than 120 minutes.

https://www.eurail.com/en/help/delay-compensation

I am aware of delay compensation options (although never claimed). But in this case how would you show/prove an intended train was cancelled? For example, if I planned to travel on a strike day I can show trains were cancelled that day, but I simply did not travel that day, so I do not have an active ticket or reservation. 

Instead, I will be left with unused travel days!

Delay compensation does not apply when you could not travel due to cancellations.

You could however claim reimbursement under EU Regulation 1371/2007 article 16 option a. (This regulation has been transposed into UK legislation.) According to this article, you're entitled to a reimbursement for the journey not made, provided the expected delay at the destination would be more than 60 minutes.

I am afraid the conditions of carriage in the UK are pretty much watertight and your chances of getting anything from the rail operating companies are just about zero. Your only avenue is to claim on your travel insurance if it covers strikes and you took the policy out before the strike dates were announced.

I'd first request a refund for the unusable days via Eurail to see how that goes. They might refer you to the operator(s); I'm not sure what the procedure is for refunds because you could not travel: Eurail does not say that but they have sold the pass so they're the first point of contact.

Fact is, AFAIK, you're entitled to:

1. A reimbursement of the travel days not used, or
2. A reimbursement of extra expenses because you had to organise an alternative, or
3. Compensation for delay if you postponed travel until directly after the strike.

3. is the responsibility of Eurail, 2. of the operator, not sure about 1. but I suspect Eurail. I'd be very curious why one would not be entitled to any of those options. "Because it’s in the T&C” is not a valid answer since legislation takes priority.

Conditions of Carriage are not terms and conditions. They are the legal framework under which an operator offers a service. The only way these can be challenged would be in court where effectively it would be individual versus HM Government. I believe there have been challenges in the past but none successful. I think only a class action spearheaded by someone like a Consumer group stands any chance of even getting it to a hearing. The rail operators in UK will never deviate from the Conditions of Carriage whether they are franchises or operator of last resort as they are all financed from the Department of Transport.

I don’t work in the railway industry now but did in the past.

In that case, I'd go via Transport Focus. But in this case, I still think the best is to ask Eurail first.