Tight international connection at Atlanta?

51 minutes at Atlanta is tight - but very doable. The US has no (physical) outbound immigration, so you'll be able to go directly from your arrival gate to your departure gate.

The problem of course is that if your inbound flight is late then you've got very little room for problems. The LHR flight you're on is the last one out for the day, so any problems with mean an overnight stay in Atlanta. Presuming you're all on one ticket (sounds like you are) the airline will look after rebooking you onto a new flight at no charge - but depending on the reason for the delay the may or may not pay for overnight accommodation. If they don't pay, that'll be up to you (or your travel insurance!) to cover.

Personally I'd be calling the airline in advance and seeing if there's any chance of changing to an earlier flight from San Diego (there's one just over an hour earlier, and one another 100 mins before that). You can also try the same at check-in if you're there early enough.

If you do end up taking the flight with a 51 minutes connection, the usual recommendations apply - try to sit nearer to the front of the plane so you can get off earlier, make sure you know where you are going (there should be a map in the in-flight magazine), and ALWAYS check the departure gate when you land just in case it changed (nothing worse than running all the way to the other end of the airport, then discovering the flight left from the gate next to where you arrived...)

Most international departures at the Atlanta airport are from a terminal separate from the domestic terminal. Virgin Atlantic to LHR seems to depart from the international terminal, and your San Diego flight would be coming in to the domestic terminal. You would have to exit the domestic terminal by taking the PlaneTrain accessible on the lower level of each terminal (A through E), go outside to the ground transportation center at the west end of the building, and take a shuttle bus to the international terminal, a 12-minute ride. While your luggage would be checked through, it may be physically impossible to make the connection. I live in Atlanta, and would find it a bit too close for comfort.

There are other options if this is a code share (or partner) between or with Delta Airlines and Virgin Atlantic. Should you miss your connection, there are two more Delta departures non-stop from Atlanta to Heathrow (7:25 pm and 10:05 pm). If you are unable to get an earlier flight from San Diego, either because of availability or having to pay to change flight plans, you might check with Virgin for reassurances that you will be accommodated by Delta.

I often do such stopovers, and 9 out of 10 times even 30 minutes is enough.

Also, the international connection will typically wait (they often start late just for that reason, and they have an hour or so buffer built in for it).

However, if your first flight is seriously late, you might miss the second one; but if it is not due to weather and other 'uncontrollable outside influences', it is the airlines problem, and they will rebook you on the next day, and give you hotel and meal coupons and pay for taxi to hotel, etc. So if you are not in serious trouble because you arrive a day later, you should enjoy a free vacation day in Atlanta. If they can blame it on weather, you are on your own. They probably would still rebook you for free to the next day, but you pay the stayover.