tl;dr: once it's booked, they should honour it or compensate (except in the case of not-at-fault delays on a minority of operators)
This is for the Eurostar, but I guess the question is general for UK trains
Nope. In fact, many of the franchised national rail operators are different to each other, let alone Eurostar.
Eurostar's have a delay compensation policy, which is set out in more detail in their conditions of carriage. The pertinent section, which sets out your rights for compensation, is section 33. In 33.3, we find the following (emphasis added):
33.3 You will not be entitled to compensation under paragraph 33 where you are informed of a delay before you purchase your ticket or where a delay due to re-routing or continuation on a different service remains below 60 minutes.
This appears to be a case of exceptio probat regulam in casibus non exceptis (the exception confirms the rule in cases not excepted); thus, if you do not fall under the exception of being informed prior to purchase, you are covered.
Please note, however, the general exceptions in section 35. These can be (broadly) summarised as no refund being due when circumstances are outside the control of the rail industry, when the passenger is at fault and in a few edge cases I can't see occurring on Eurostar (e.g. journey entirely outside EU).
We also need to consider section 17. This sets out your rights for rebooking/cancellation in the event of a timetable change after booking. It also contains the following exclusion:
We do not guarantee the train times to you and they do not form part of your contract of carriage with us. It is your responsibility shortly before you travel to check for any changes to the timings for your train.
First, it's important to note that section 17 does not make any provision to override or invalidate 33, so I think you should still be covered under that. I think this exclusion exists to stop you suing them for breach of contract and consequential losses in the event of such changes. It may also be significant that the exclusion is from the contract of carriage, not the conditions of carriage, so I don't think that will have any bearing on the applicability of 33.3. However, it would be interesting to hear from anyone that has experience of having tried this.
Finally, we have this favourable rule in the preamble, supporting the belief that 13.3 prevails over 17:
Where there are any inconsistencies within these Conditions of Carriage, the condition more favourable to the passenger will apply
These rules implement/are subordinate to the PRR and the CIV, so you have any rights which may arise under those and could enforce them against Eurostar if they do not comply. You would also have access to the standard (un)fair trading/consumer protection etc. rules of the country in which you booked.
Consequently, it seems that any ticket rescheduling after you have booked constitutes a delay; thus, if you do travel, you will be entitled to the regular compensation. The delay time quoted in the automated email may well be as innocent as the rescheduling falling through the cracks in their computer system - if it makes a material difference to a claim, I would recommend speaking to them in person/on the phone/via email.
This includes most (but not all) domestic rail services in Great Britain. The compensation specifics vary between train operators, but (apart from the older franchises, like GWR) most are now on some variant of the "delay repay" scheme. On this scheme, you are entitled to a sliding scale of compensation, increasing as the delay increases, whatever the cause of the delay. For some operators, this kicks on on delays as short as 15 minutes.
Some franchises are not yet on this scheme, and have less generous compensation arrangements. GWR, for instance, do not compensate for delays "outside [their] control". They also have different arrangements for season ticket holder than the delay-repay operators. For the rest of this discussion, uncited statements come from GWR's passenger charter; it should be representative of the least generous operators.
Advance tickets can be purchased up to 12 weeks in advance; planned engineering works are booked at least 12 weeks in advance. Thus, they will be known about when you book your ticket, so no schedule change required. (I can see an edge case, if you can buy a 30 day open return for outward travel in 12 weeks time - I don't know if you can do that, but I think you'd take the risk of engineering works in that case; this is also the case for long-duration season tickets.) Emergency/short notice engineering works count as a delay, the same as any other. Delay-repay operators should repay, for others it depends (e.g. if the works were to repair vandalism, you wouldn't be covered, but if to fix faulty points, you would be). In addition, you may be entitled to cancel your travel plans for a full refund, even where the ticket doesn't usually allow this.
National Rail Enquiries has links to the compensation rights and passengers' charters for all train operators.
Open Access Operators
A small minority of services on the national rail network are operated by open access operators - these are train companies that pay for access to track/facilities, rather than operating under contract to DfT. These include Grand Central, Hull Trains and Heathrow Express. In theory, these are a law unto themselves, but in practice I think they're comparable to their franchised brethren. Check the relevant operators websites for details.