Wragg was brought up in Slough, England and started working in a bank as a young man. His hobby was model-making and when his father's company had a contract with Gerry Anderson's puppet film company AP Films, Wragg worked for them as an assistant and later as an effects designer on shows including Thunderbirds and Captain Scarlet and the Mysterons.
Moving to the BBC, Wragg worked on many iconic programmes, such as Doctor Who, Allo Allo!, Filthy Rich & Catflap, Bottom and The Two Ronnies. Grant Naylor Productions recruited Wragg for Red Dwarf because of his extensive work with models.
Wragg created many of the show's models, including Starbug, Blue Midget and Red Dwarf itself. Although writers had some ideas for the ship, such as the Front Ramscoop, Wragg came up with other ideas, such as the embedded meteorites to make the ship appear less conventional, older and more travelled. He was also responsible for destroying the original Red Dwarf model for the Series V episode "Demons and Angels".
One of Wragg's other creations was the make-up and prostehtics used by David Ross and later Robert Llewellyn for the mechanoid Kryten; Wragg worked with make-up designer Bethan Jones in developing the mechanoid masks.
Wragg enjoyed working with water, creating many underwater scenes and model shots. Craig Charles joked that Wragg needed little excuse for putting on his wetsuit, even doing it when it was simply raining.