It was largely the work of the British Whig statesman Thomas Pelham-Holles, 1st Duke of Newcastle, who considered an alliance with Austria crucial to prevent the further expansion of French power.
In 1725 Austria had signed the Treaty of Vienna, offering material support to the Spanish in their efforts to try to recapture Gibraltar from the British.
That cleared the way for a full rapprochement between London and Vienna and gave the Duke of Newcastle more control over British foreign policy.
The British had also applied diplomatic pressure to persuade Prussia's Frederick the Great to agree a ceasefire at the Treaty of Dresden so that Austria could turn its full attention against the French.
The worst was during the Congress of Breda, aimed at negotiating an end to the war and leading to the eventual settlement at Aix-la-Chapelle in 1748.
The Austrians had an enthusiastic supporter in Newcastle, Whig politician Thomas Pelham-Holles, and apparently had no other major ally to turn to.
Britain, left out in the cold, made a hasty alliance with Prussia, hoping that the new balance of power would prevent war.
In spite of its efforts during the war, Austria was ultimately unable to retake Silesia, and the 1763 Treaty of Paris confirmed Prussian control of it.
Britain and Austria later again became allies during the Napoleonic Wars, but they were both part of a broader anti-French coalition, and the relationship was nowhere near as close as it had been during the era of the Alliance.