I recall when I used to commute on the single-track line between Oxford and Charlbury. In the evenings, my train out of Charlbury would be held if the busier train from London was delayed and had missed its 'slot' on the single track. The delayed busier train always seemed to get priority, even if it meant holding back and delaying a service that was running on time.
May I enquire on the types of trains you are talking about from your post, if it's a 1/2 car DMU against an HST, then, the HST will ALWAYS get priority, and it's been like that since B.R. days, I appreciate nowadays that the reporting codes have changed, but, years ago a 2/3 car MU/DMU local pax service operated under a 2 headcode, a mainline HST or 10 coach pax service had a 1 headcode timed to run faster than a local and given priority, however, times have now changed to quite a few more single branchlines than in decades gone by, and of course we now have single coach passenger workings, Class 153, for example, I suppose it's the bigger the train the bigger the delay factor that governs signalling operatives and train management.
The other thing of course, is that a Class 1 passenger train could run at speeds in excess of 100 mph, years ago no DMU could ever reach that speed and were given a class 2 headcode accordingly, nowadays, DMU's can go faster, Class 170 for example has a top speed of 100mph and therefore operate under class 1 regulations.
In reply to the OP, I presume if we are talking about only a 1 minute delay, it would appear bizarre that any connecting services are not held, even if it is a different TOC, but, as has been the general case ever since privatisation and was pointed out by Jimini, the general response is, hard luck it isn't one of our trains that's been delayed, you'll have to wait for the next one, which has been the biggest frustration factor since all TOC's were formed.
Cheerz. ex-railwayman.