Connection time to another flight in Atlanta when returning from Manchester England

Atlanta is fairly easy to navigate and getting from the international terminal to your departure terminal will be very easy using the "plane train". With Global Entry, your processing should be fairly quick. The only real unknown is the weather. August is prime season for afternoon thunderstorms that can cause arrival delays. To be safe, I'd look for a three hour connection window. That might sound like overkill to some, but I'd rather have extra time and be bored, than short on time and stressed about making a connection.

I see Virgin sells a Manchester-Atlanta-Nashville ticket with 2 hr 15 min stop in Atlanta.

If they are selling that, then that should be sufficient time.

Is that what you are looking at?

Adding: what time of day does the international flight arrive? Last week (just before the big freeze and storm) I flew Delta through Atlanta, although from Argentina. Yes, since Atlanta is your first US entry, for customs and immigration.
That first flight was on time, and I had booked a 3 1/2 hour connecting time for the Delta flight to SEA. The airport was fairly quiet at 7:30 am when I came out of the jetway thing. I checked with the Delta desk there and was able to get booked standby on the earlier flight I didn't choose but had preferred.
I have the CBP app, and also didn't need to collect a checked bag. The line was really, really long for immigration, but only me in the CBP lane! I zipped through, and that plane train is fast and efficient.
So if all goes smoothly...and assuming this is all on one ticket,, correct? The apps if you don't have them are very helpful.

August is prime season for afternoon thunderstorms that can cause
arrival delays.

Or departure delays.

You can say that again. In 2002, I flew from Denver to Atlanta to Stuttgart (Delta had an Atlanta to Stuttgart flight, because I wanted to land as close to Rothenburg, my next destination, as I could). Because of a thunder storm we were an hour late leaving Atlanta so I got too late into Stuttgart to take a regional train and had to use a more expensive IRE an hour later.

But in your case, I'm sure there are many flights from Atlanta to Nashville, so if you miss your scheduled flights they'll put you on a later flight. At worst, you'll have to rent a car and drive to Nashville. I used to live in Nashville, and have made that trip by car many times.

What is not clear is whether you are buying your trip as one true connected flight or are looking to add a separate flight to Nashville on to an already booked MAN-ATL flight. If you have a booked everything on one flight then Delta should book you on the next available flight should the first flight be late or there are significant delays at ATL. If you are planning to book the Nashville flight separately you need to leave much longer as if the first flight is late and you miss the second you will have to buy a new ticket at the walk up rate.