Praised for his successes on Bellona, in 1749 he was given command of the expedition to the Pacific by the sloop Porcupine and Raven, then of one to the north-west and north-east passages in the Atlantic, both of which were proposed but then called off for political reasons.
Meanwhile, in about 1747, Campbell had his first direct involvement in the development of astronomical navigation, as the first person to use a Hadley quadrant to measure the angular distance between the Moon and fixed stars.
His next commands after Bellona were Mermaid, Prince (90 guns) and – in 1757 – Essex (64 guns) under Edward Hawke in the Bay of Biscay and the blockade of Brest (barring an interlude in 1758/59, as flag captain to Anson in Royal George when he temporarily took over command of the Brest fleet).
During Campbell's command of Essex, in 1756, James Bradley suggested to the Board of Longitude (chaired by Anson) that Campbell should give a sea trial to Tobias Mayer's new lunar tables and reflecting circle, and Campbell did so successfully within sight of the French coast, 'though they [the observations] were not taken with all the advantages that might have attended them, had I been alone; for I was all the cruise in company with an admiral whose motions I was obliged to follow',[3] in trials which would profoundly influence marine navigation for the next 250 years.
He compared Mayer's new reflecting circle instrument with the common wooden Hadley octant as means of observing lunar distances, and in doing so found Mayer's was much too heavy whereas Hadley's – though it could not measure angles beyond 90° and was often unstable in its wooden frame – was far more useful.
On 25 June, the Franco-Spanish combined fleet commanded by Luis de Cordova intercepted Portland, which was escorting another 27 ships.
During this time he returned to Britain periodically, allowing him in 1784 and 1785 – at Hans Moritz von Brühl's request – to arrange trials of Thomas Mudge's first chronometer on his passage to and from Britain and in Newfoundland (borrowing an achromatic telescope from the Board of Longitude to ascertain Newfoundland's longitude).
Also, as a result of Campbell's proclamation of religious freedom for all inhabitants of Newfoundland, Bishop James Louis O'Donel authorised the construction of a Catholic church.