The issue of herd immunity that matters is the effect on the Rt number with NPIs reduced to an acceptable level - because if that is >1, cases will rise. Fauci posited a herd immunity percentage of between 70% and 85% but merely pointed out reaching it would not be a cliff edge thing. And without vaccinating under 18s, those figures will be difficult to achieve in UK (67M total, 14M under 18s, 3M unables, 50/67 is (only) 75%. Could increase that by including the number of under 18s who have post-infection antibodies.
In UK (and the USA) there'll be regional disparities - I hear that vaccine take-up in JCVI Gps 1-9 in the SW is 97% whereas in London it's 86% [Edit: but in London there'll be a much higher percentage of under 50s who have post-infection antibodies]
As the percentage of the population still susceptible (un-vaccinated or without sufficient antibodies from previous infection) decreases, the transmission chains should be obstructed.
The measles v flu similarity will depend on whether the various vaccines have sufficient effectiveness [v transmission] against emerging VoC (and the jury will need to sit a while longer for that). A tweaked set of vaccines for an autumn booster to protect the more vulnerable third of the population against disease severe enough to require hospitalisation will serve to minimise that outcome for them and allow the NHS to provide the treatments for all the other ailments, within resources.
But if the world's vaccine supply remains a limiting factor, giving 20M doses to those in UK in September will be at the expense of saving many more lives in countries where case rates of COVID-19 are still high. I don't know where the balance lies.