The story screens at 4:30pm in both countries. New Zealand has an additional screening on Monday 10th June at 4:45am.
The UKTV billing describes Vengeance on Varos as follows:
Seeking the rare mineral Zeiton-7 to repair his TARDIS, the Doctor arrives on Varos, a world where political prisoners & their guards are all subjected to sadistic tortures.Vengeance on Varos was first broadcast in Australia in 1985. New Zealand did not get to see it until 1989. The story was originally screened in Britain as two 45-minute episodes, but was first broadcast in Australia and New Zealand in four parts. The UKTV transmission will feature the two-episode version of the story.
UKTV is showing stories throughout the year in the lead-up to the anniversary in November. Colin Baker's sixth Doctor is the focus of the stories screened during June. The remainder of the schedule includes: The Mark of the Rani (16 June), The Two Doctors (23 June), Revelation of the Daleks (30 June).
Up-and-coming broadcasts from both 20th and 21st Century series of Doctor Who can be found via UKTV's Doctor Who sections for Australia and New Zealand.
(Note: An earlier version of this article reported that New Zealand would receive another showing of Attack of the Cybermen on 9th June. Although the story appeared on the UKTV schedule, it was not screened. Instead the episodes Bad Wolf and The Parting of the Ways were shown.)