Excluding Gibraltar.
I have never heard of any such ideas. The British standard policy regarding Europe in the 18th and 19th century was the prop up anyone fighting a possible hegemon, to make sure there were no challengers to their naval supremacy.
The British monarch was the reigning monarch of Hannover (initially Brunswick-Lüneburg) from 1714 with George I and thus had a convenient excuse to intervene in any conflicts in the Holy Roman Empire (or related to it) should they need to.
Nations during this era attempted to annex land if it was to the benefit of those who ruled - in Britain the elite was a combination of landed aristocracy and merchants (during the era many of the latters were owners of sugar estates in the Caribbean or parts of the East India Company).
Hannover did not provide any funds for the British treasury (the monarchs had promised that any revenue raised in Jannover would stay in Hannover) nor any armed forces (the local forces were only to be used for local defence), but did provide access to the mercenary market in Germany, which allowed the British to raise the Hessians and the King's German Legion, both of which were used in the American Revolution.
During the Belgian crisis in 1830, when Belgium revolted to free itself from the Netherlands (to which it had been merged in 1815), the French ambassador to Britain (and later foreign minister of France), Talleyrand suggested a partition plan to resolve the crisis by partitioning Belgium.
The plan failed since no powers wished to see the French gain territory so soon after the Napoleonic war, and because Britain was completely uninterested in assuming responsibility for the defence of the Free State of Antwerp.
Bottom line - no, the British never had any interest in annexing parts of continental Europe. Their interest in expansion during the era laid in India foremost, as they coudl extract massive revenue there. Annexint territory in Europe would have meant requirements in defence, fortification consctruction and handling problems, nationalist sentiments and perhaps even revolts in non-English speaking parts of Europe, while setting Britain up to be dragged into wars over that territory - wars she had no real interests in fighting.