The Peto cross detent is rare form of chronometer escapement.  It was seldom used despite the theoretical advantage of having the detent spring in tension as in an Arnold type detent but still retaining an escape wheel without friction.  Brockbanks appear to have appreciated the qualities of the escapement and used it more frequently than other makers.  The firm was formed by two brothers in 1781, John Brockbank, 1747 - 1806 and Miles Brockbank, 1754 - 1826.  By the late 1780's they concentrated on making chronometers becoming the largest supplier.  Thomas Earnshaw was employed by them.  See the December 2015 edition of the Antiquarian Horological Society for an article about Brockbanks.  This example has a case and dial made for it in USA.  

Interestingly a watch with the preceding number was part of the Ilbert collection, and is now in the British Museum.  The movement, also with a Peto cross detent, is almost identical and housed in gold pair cases hallmarked 1800.  It is illustrated in the Catalogue of Watches in the British Museum. Vol. VI.