Slarvian

Slarvians were a species from Slarvia (PROSE: Project Wildthyme), described by the Fourth Doctor as "huge bionic snails" (AUDIO: The Eternal Battle), and dubbed by Iris Wildthyme, "slime-filled Slarvians". (AUDIO: The Iris Wildthyme Appreciation Society) The First Doctor heard tales that the Slarvians enslaved whole planets. They also had a base on Slarvos. (PROSE: Childhood Living)

History
They made several attempts to join the Galactic Federation by the 20th century, but had been denied entry.

They attempted to colonise Earth in 1979, but they were stopped by the Doctor, Susan, Edward Grainger, Linda Grainger and Guy Oliver. (PROSE: Childhood Living)

In the early 2000s, the Forge harvested a Slarvian from a peace conference. (PROSE: Project: Valhalla)

In the 42nd century, the Slarvians tried to invade the New Naxium Empire, but they were thwarted by Iris Wildthyme and Panda. (AUDIO: The Iris Wildthyme Appreciation Society)

Other references
The Third Doctor once told an amusing anecdote to Alistair Gordon Lethbridge-Stewart which involved a Slarvian in a Santa suit holding a rubber chicken. (PROSE: Faithful Friends: Part 1)

The Fourth Doctor claimed that a Slarvian had once asked to become his companion, but he refused, saying "it never would have worked". His main reasoning involved slime in the TARDIS control room. (AUDIO: The Eternal Battle)

While living a simulated life of fame and fortune in the Pleasure Prison, Panda told an amusing anecdote involving a Slarvian and a man wearing a Quark suit in a bar. (AUDIO: Whatever Happened to Iris Wildthyme?)

The Forge's base in the 22nd century could withstand the combined forces of the Dalek, Slarvian, and Cyber empires. (PROSE: Twilight's End)

An Auctioneer said "let the dog see the Slarvian". (COMIC: Space Invaders!)

Broteas demanded Slarvian oysters as sustenance under Shadow Proclamation law. (COMIC: Bloodsport)

had plans to steal the Slarvians' Astral-Core. (PROSE: Lords and Masters)

Behind the scenes
The Slarvians were created by Mark Wright and Cavan Scott for an abandoned Big Finish Productions project. They were first mentioned in the Scream of the Shalka sequel short story The Feast of the Stone, where the Ninth Doctor makes a joke involving a Slarvian and a "fellah in a Quark suit" at a bar. However, their first actual appearance was in Mark Wright's audio drama The Slarvian Menace, part of the Big Finish Productions' The Tomorrow People series.