I never found many records of this kind of music. It is light sounding, well performed and recorded and of an interesting period. Baroque music for ensemble. And Trevor Pinnock is one of the best.
According to the liner notes, England of the early eighteenth century was looking to Italy for musical influences. France and Germany were no longer that interesting, maybe they were looking too much at their own past in those years.
The piece from Geminiani is another version of the popular piece from Corelli (say the liner notes), the Folia. About that piece a lot of studies have been made. It is not from Corelli, but might be from Lully. It has been used by over 150 composers of all time. Rachmaninov tried his hand at it in his Corelli variations, Beethoven used in his second part of the fifth symphony and more recent version can be heard in Vangelis’ Conquest of paradise.
Try this version and see if you can recognise it.