Churchill could have his next start in the Qipco Irish Champion Stakes at Leopardstown on September 9.
The dual 2000 Guineas winner, who was forced to miss the Sussex Stakes following a downpour at Glorious Goodwood, ran with credit at York when finding only Ulysses too good in the Juddmonte International, on what was his first try at a trip beyond a mile.
Trainer Aidan O'Brien said: "We were very happy with Churchill. When we missed Goodwood, it just messed us up a little bit, but we we're very happy with the run. I would imagine that he'll come forward from it."
When it was put to O'Brien that he stayed the extended mile and a quarter well, he added: "I'd say he did. He was never a horse to wilt, anyway. I think the run will bring him forward.
"We're thinking of the Irish Champion, but we'll see how he is."