Within the UK, there's no difference whether you buy a CIV or normal ticket in terms of protection for delays coming
from Europe.
Eurostar are generally pretty relaxed in regards to reorganising you onto later services if needed from what I've read in the past. The main thing they recommend is getting some evidence of the delay from a member of staff (for paper tickets this could possibly be an endorsement on the ticket, for example).
Q: Can a passenger travel on any trains other than the one on which they are reserved, without changing the booking?
A: In certain cases, yes but the following principles must apply:
[...]
Once the journey has begun. If the passenger is delayed and the rail industry or its partners (as shown below) is at fault, which should be checked with your Control Office, change to another train of the same company is allowed to get them to their destination with the least delay.
This is irrespective of combinations of rail tickets held. Examples are:
[...]
- Combination of Eurostar tickets into the UK and then either advance purchase tickets from London Terminals or “London Intl CIV” or “London Eurostar CIV”.
Whether staff are aware of this or not, who knows, but it's on the internal knowledgebase!
The main benefits are extended validity for tickets to London Intl., relaxed restrictions, etc.