What aircraft was used as Air Force One for the flight between Southampton and Shannon?
As Bianfable mentioned, this is the C-32A, which is the U.S. Air Force's transport variant of the Boeing 757-200.

In this case, due to the shorter runway, they used the C-32A instead of the iconic VC-25, which is the Air Force's VIP transport variant of the Boeing 747-200 that is typically used for transporting the President of the United States.


U.S. Air Force C-32A. Image Source: Wikipedia  

The C-32As are mostly used for transporting the Vice President of the United States as "Air Force Two" as well as members of the President's family and other high-level government officials.

However, the President may use the C-32As when flying to airfields that are too small to adequately support the monstrous VC-25s. The short-field performance of a 757 — especially a VIP-configured one — is quite good, so it can use runways that are relatively short for a plane of its size. It is also capable of making trans-Atlantic hops non-stop from the U.S. East Coast (indeed several airlines use the 757-200 to do that with much more dense passenger loads.)