Green’s Dictionary of Slang

wellie n.

also welly, welly-boot, wellygog

[1950s+] a wellington boot.

In phrases

give it some welly (v.) [abbr.; phr. underlined by an extra image of the ‘wellie-chucking’ contests that have become popular]

[1970s+] to apply more force, energy or effort.

give someone the welly (v.)

[1970s+] to reject, to get rid of; to dismiss.