The contracts awarded to individual train operating companies (TOCs) specify when they must pay out for delays. (i.e. the length of time that you're delayed, before a compensation payment can be triggered, varies between different companies). However, with the exception of Great Western and Chiltern (where their contracts permit them to refuse compensation for delays beyond their control), all TOCs are obliged to pay out regardless of the cause of the delay.
If you've bought a
through ticket for a journey that uses the services of several different TOCs, you can seek compensation from just one of them. (That would normally be from the TOC that operated the first sector of your journey). You do NOT have to submit multiple applications. The system simply looks at your delay upon arriving, irrespective of how many different causes there might have been along the way.
Fr example, if I start a journey from my local Great Anglia station and arrive at my destination (having used the services of several TOCs) more than 2 hours later than I should have done, I can claim the full costs of my ticket back even if it was a return ticket (and even if most of the delays had nothing whatsoever to do with Greater Anglia's services):
http://www.upl.co/uploads/Delay1574546077.jpg
However if you've used 'fare splitting' and bought separate tickets for the services of different TOCs, you'll need to claim for each sector separately.
For example, if I buy a through single ticket from Ipswich to Brighton and I get delayed on the Ipswich to London section (causing me to arrive over an hour late in Brighton), I can claim the whole of my fare back. However if I buy separate tickets between Ipswich and London, and between London and Brighton, I can only get a refund on the Ipswich to London sector, as trains between London and Brighton were running normally.