One of many homages to famous sci fi is the name of the garage, HG Wheels, a play on the name of "War of the Worlds" author H.G. Wells.
The supermarket that Lu-La and Shaun visit is named Milliways, a nod to Milliways, the Restaurant at the End of the Universe from "The Hitchhikers Guide to the Galaxy."
The brief film clip showing on the TV sets in the shop window near the beginning of the film is from Nick Park's very first Wallace and Gromit short film, Wallace & Gromit - Alles Käse (1989).
The film invokes "2001 - Odyssee im Weltraum (1968)" on several occasions, including the use of its musical score and the framing of a piece of toast popping up from a toaster in a way that looks like the obelisk at the beginning of Kubrick's film.
Rocky, the rooster from Aardmans film "Chicken Run - Hennen rennen (2000)," makes a brief non-speaking cameo in one scene. He is standing on a wall holding a coffee mug (which he drops) with his name on it.