Now transformed under the leadership of Eddie Jones and winners of back-to-back Six Nations titles, England were paired with European rivals France and band three powerhouses Argentina during the 10 May draw in Kyoto.
Wales were drawn in Pool D, alongside Australia - for a second successive World Cup - Georgia and "America 2", while Scotland and Ireland are in Pool A, alongside hosts Japan and a play-off victor.
Scotland, who were in Band Two thanks to their current world ranking of fifth, could have drawn New Zealand, England or Australia from Band One, and Italy, Georgia or Argentina from Band Three.
The Brave Blossoms stunned South Africa two years ago in England, however, and will certainly not view reaching the knockout stages on home soil as mission impossible.
The group will be rounded off by yet-to-qualify teams from the Americas - likely to be one of Uruguay, Canada or the US - and Oceania - likely one of the Pacific Island power-houses, who themselves are no pushovers.
"We know South Africa very well", added Hansen, looking ahead to New Zealand's first ever group clash with the Springboks, who memorably beat the All Blacks in an emotional 1995 final.
The other two teams in Pool D are not yet known for certain but will be one of Fiji, Tonga and Samoa as well as either the United States or Canada.
"It's not a bad group I'd think", said Williams.
Today, Ireland were drawn alongside Scotland and Japan in Pool A for the 2019 World Cup. We will have to wait and see.
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Japan will be reunited with the Scots, who they lost to as they exited in the pool stage in 2015.
When does the 2019 Rugby World Cup start?
Australia, twice champions and the 2015 runners-up, will become reacquainted with Wales in Pool D, which also includes 11th-ranked Georgia.
The ninth Rugby World Cup, the first in Asia, will take place from Sept 20 to Nov 2, 2019.
While few tournaments play out exactly as planned - for example England's demise in pool play at the last edition - should the All Blacks top their group, they will likely face Scotland in the quarterfinals. On the other hand, we know Ireland pretty well and have a couple more opportunities to play them before the World Cup, while we also know a lot about their players through the Guinness PRO12.
Prior to the draw taking place, World Rugby voted to increase the period of residency to become eligible for an worldwide team from three to five years.
As one of the top seeds [fourth in the rankings], Joe Schmidt's men were drawn in with hosts Japan, Scotland and the victor of qualification matches from Europe and a play-off.
New Zealand will face South Africa in the upcoming 2019 RWC pool stage along with Italy.