T5291 was a four-blade left-hand tractor propeller used on B.E.2c and d, R.A.F 1a engine (on D.H.6 as well). Such a propellers were produced by many contractors (e.g. Aldam Heaton, Integral, Lang).
LP1020A was a two-blade right-hand tractor propeller used on Bristol Scout and Sopwith Pup, 80 hp Le Rhône or Clerget engine (known makers Morris & Co and Sage & Co). "Short nose" should be propeller shaft variant (there are at least three Le Rhône 9C versions - "short", "medium" and "long"). The pitch of 2430 mm is listed in R. C. Gardner's database of British Propellers.
Regards,
Yavor
P.S. Darracq produced propellers like T7928 for D.H.2 and R.A.F. F.E.8 (Le Rhône 9J, Gnome Mono), and T1708 for D.H.5 (Le Rhône 9J, Clerget).