The best book I found of early rifles in the British Army is 'British Military Flintlock Rifles 1740-1840' be De Witt Bailey. In the chapter on 1793-1802 he gives examples of various rifles that may have equipped the numerous foreign rifle units in British pay. Including Dutch 1798 Batavian Jaeger Rifles and what he refers to as 'The Prussian light infantry rifle musket 1798-1800' which he says were a mixture of components from earlier Prussian weapons put together by Schickler brothers at the Potsdam arsenal.
There is little evidence as to what unit had what weapon. From 1798 as well as the fully rifle armed 5th battalion the 60th the regiment began to convert the light companies of the the other 5 battalions to rifle companies. Later inspection reports do mention those companies having a wide range of rifles or different types and calibers. The 5/60th received the Baker rifle in 1803.