To get at the official position ATC adopts, read CAP 493 (Manual of Air Traffic Services Part 1), Section 5 Chapter 3. This covers overdue action. If an aircraft which has filed a flight plan (VFR or IFR) and a departure message has been sent, fails to arrive within 30 minutes of its due time, it's pretty clear that there may be a problem and overdue action will start. It's less clear, if the pilot has phoned for PPR and given an ETA and then doesn't show up.
I work at a FIS field (there's a similar publication to CAP493). I would take seriously a no-show on an activated VFR plan and, after verifying departure and alternates, start the overdue procedure. For a flight with only a telephone ETA, I have many times checked up on a no-show at ETA+30 only to find that he had not departed, departed late, or decided to go somewhere else. I have never found such a flight to have had an accident. So, in the absence of other information, I would be reluctant to start overdue action.
Consider -- you depart on a 2.5 hour VFR flight with activated flightplan. You like to operate without a radio and, 30 minutes into the flight, you crash without speaking to anybody. It would be a further 2.5 hours before your destination field/responsible person even considered any form of overdue action. Plenty of time to die from hypothermia. Avoid this by talking to or just listening to air traffic agencies en-route.
Further consider -- if you divert due to weather or just on a whim, tell the diversion ATC that you are on a flight plan so they can report your arrival. If not on a flight plan, but having given an ETA, phone your destination field an tell them you have diverted.
OP, do read the above reference (available on the CAA web site), it will make clear what you can expect.
Alan.