Gatwick opened in 1958. Given that financial support was being given to US military-connected families by a US agency, I would expect the carrier to certainly be from the US. Jets from New York (Idlewild/JFK, not La Guardia) to Chicago started in 1959 by all three of American, TWA and United, 707 or DC8 and generally continuing to the West Coast.
US transatlantic charter operators (given it was Gatwick) ran in the late 1950s still a lot with DC4s, changing in the early 1960s to Constellations, which came onto the secondhand market before DC6Bs, while DC7s were just too complex and unreliable. It's a hunch only but I would guess Connie Gatwick-Prestwick-Gander-Idlewild, then a jet to Chicago.
Regarding the turboprop Viscount, and later Electra, US operators did have the habit of misleading by branding these as JET powered, with JET written very bold, and powered, or prop, not at all so.