Could your mystery frame be a Sun Wasp? This is very similiar: https://www.ebay.co.uk/itm/Sun-Wasp-1940s-Bike-Patina-shop-window-garden-flower-arranging-display-prop/152478974503
Very possible it's a sun wasp! I think parkes & sun cycles are the same company, parkes being slightly better made from what I have read online. So it would make sense in both names using similar Lugs
@Nbenja3 started
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Could your mystery frame be a Sun Wasp?
This is very similiar:
https://www.ebay.co.uk/itm/Sun-Wasp-1940s-Bike-Patina-shop-window-garden-flower-arranging-display-prop/152478974503