That's a tight connection on your arriving flight since you'll have to go through customs & immigration here in Atlanta. If everything flowed smoothly, I think you have enough time. But it there is any hitch along the way, you could be in trouble.
On your arriving flight, the consequences of missing the connection are slight. Since you're just continuing to Miami and Delta runs multiple flights to the Miami area every day, odds are you'd just be bumped to the next flight with open seats. If you have the ability to change your flight, I'd opt for a longer connection. Otherwise, I think you'll probably still make it and if you don't would just have to face the inconvenience of waiting on the standby list for seats to open up on later flights.
On your departing flight, the consequences of missing the connection are steeper since there are fewer London flights each day, but you won't have to deal with customs and immigration. 1:25 is plenty of time for a connection in that case.
You can read more about the customs & immigration process in the Top Question on the right titled "What is the customs & immigration process when I arrive on an international flight?"