Lets use the example in the OP...

EI DUB-LGW Arrives 25 minutes late, by the time Terminals have been changed, security recleared and the Gate reached, the flights closed... BA Gate Staff: "Sorry you've not made it ontime Mr barnstaple we note your on one ticket however the connection was below the legally accepted Connection Time and as such neither ourselves or Aer Lingus are liable to rebook you, you'll need to speak to your travel agent." Would you want to have to deal with that as the Customer?