There are probably three tunes in the English repertoire that refer to Philip Astley who was a cavalryman and is credited with starting the first circus in England. Sometimes the name is corrupted to Ashley when it appears in hand written manuscripts.
Astley's Hornpipe was evidently the most popular tune as it appears in many musicians' manuscript books including John Clare, George Spencer, James Winder, William Mittell, John Miller and also in a Frank Kidson owned manuscript. Astley's Ride and Astley's Flag appear less often.
Where to find it
Astley's Circus is well documented as this list of links indicates.