Section31 of the 1988 Road Traffic Act states that the Secretary of State may authorise or provide for authorising a cycle race on a public highway. In practice it a senior police officer who actually authorises a cycle race. The act also gives the police the power to stop or divert other traffic. In general the police are happy to allow a time trial to go ahead without closing the road providing that it confirms to the rules of the sport's governing body . But it would be very unusual for tthem to permit a massed start race without, at the very least, a rolling road closure around the peloton.
Competitors like to compete on fast dual carriageways because they gain speed from the wind of passing cars. Some of the more ambitious ones try, against the rules, to increase this advantage by forcing overtaking vehicles to pass them more closely. That obviously puts hem at greater risk of a, usually fatal, acident.
Do they put up warning signs to alert motorists to the TT being run? Cyclists on extra urban DCs are not that common so some kind of warning would help a lot, it is possible that the 19 year old driver had never seen a cyclist on the A1 and had not realised this was a possibility.
Given the cyclists are doing a TT they are not going to be pootling along at 5-10mph so at least the speed differential is probably no greater than a slow goods vehicle or farm equipment. It should be possible for a cycle TT to be run reasonably safely on a quiet DC, I can understand ed_m's point about passing on SCs so perhaps with preparation a DC would be better. The other alternative is to hire/pay for a track as car drivers do for track days.