I can't find him indexed at The Athenaeum or Art Renewal Center. In fact, I had never heard of him until I was browsing galleries in the Portland [Oregon] Art Museum and came across a portrait by him.
My ignorance nothwithstanding, Sir William Beechey (1752-1839) was highly successful in his day though overshadowed in history by his flashier contemporaries Sir Henry Raeburn (1756-1823) and Sir Thomas Lawrence (1769-1830).
The Wikipedia entry for Beechey linked at his name above notes that he had 18(!!) children over a period of about 30 years by his second wife. As a demographer, I find this statistic fascinating: that approaches the maximum possible, even with two children perhaps having been twins. It has been years since I researched this, but as I recall, some women reportedly have had more than 20 births -- including some multiples per pregnancy.
As for his art, Beechey was certainly competent at portraiture, as the images below indicate. Had it not been for Raeburn and Lawrence with their greater painting flair, he probably would have been better known today.