Another quick experiment - I searched the content of the Dictionary of National Biography and again very many references to French privateers and very few to British privateers.
I DID find one seemingly very succesful British privateer captain - Thomas Goodall.
Quote:
. . . . . On his return to England, he is said to have been appointed to the frigate Diadem, but he does not seem to have joined her; he was certainly not entered on the ship's books. He accepted the command of a small privateer, and continued in her until the peace of 1801, during which period he was said to have made more voyages, fought more actions, and captured more prizes than had ever been seized before in the same time by any private ship.
When war broke out again, Goodall fitted out a small privateer of ten guns and forty men, in which, on 25 July 1803, he fell in with, and after a stubborn defence was captured by, La Caroline, a large privateer, and again taken to Lorient. He and his men were sent on to Rennes, and thence to Espinal, from where he escaped with one of his officers. After many hardships and adventures they reached the Rhine, succeeded in crossing it, and so made their way to Berlin, whence they travelled on to England.
On the outbreak of war with Spain, Goodall again obtained command of a privateer, and in her captured a treasure ship from Vera Cruz. He afterwards touched at San Domingo, and having made some acquaintance with Christophe, one of two rival black leaders engaged in a civil war, he was induced to put his ship and his own services at Christophe's disposal. His assistance may have turned the scales in Christophe's favour. Goodall was considered by the governor of Jamaica to have acted improperly, and so was sent home in 1808. On his arrival he was released, and shortly after moved to Haiti—he claimed he was ‘Admiral of Hayti’—coming home in 1810 and again in 1812.
Goodall was said to have remitted to his agent in England—William Fletcher, an attorney—very large sums of money, totalling £120,000. The amount was probably exaggerated, but it seems clear that it was considerable. However, he now found himself a bankrupt by the chicanery of Fletcher, who had not only robbed him of his fortune but also of his wife; although the mother of eight children by Goodall, six of whom were living, Charlotte had become Fletcher's mistress. In July 1813, Goodall brought an action for ‘criminal conversation’ and it was deposed at the trial that during her husband's imprisonment and absence Mrs Goodall had supported her family by acting; but there was no suspicion of misconduct by her until she was seduced by Fletcher. The jury, taking this view, awarded the injured husband £5000 damages. Nothing further is known of Goodall, but it would seem probable that he lived privately until his death, which is said to have taken place in 1832.
P - I think you may be right about many British merchant ships applying for Letters of Marque - "just in case". This would cover them legally if they should happen to meet with an enemy and have a chance of capturing it.
MB