Gelson was not swept away by the good news before him, the sole benefit of devouring the Ottoman Empire seemed great, but to bolster the Ottomans to contain Austria was not something the United Kingdom alone could achieve.
Now that the Ottoman Empire was in decline, the Vienna Government could observe with indifference, allowing them to act at will. Once the Ottoman Empire showed signs of resurgence, the situation would immediately change.
If one day the Vienna Government suddenly took a notion to remove this thorn in their side, the British were actually quite powerless.
The London Government could not possibly go to war with the Austrians for the sake of the Ottomans, regardless of whether they won or lost, it would simply play into the hands of the French.