Both sides have qualified for the cup quarter-finals.
England and Wales both enjoyed an unbeaten opening day at the Emirates Airline Dubai Sevens to top their respective groups and qualify for the cup quarter-finals.
Defending champions England will face New Zealand in the last eight while the reward for Wales, who also reached the quarter-finals in Australia last week, is a showdown with Argentina.
Dan Norton was the star of the show for England, scoring twice in a 43-0 rout of Zimbabwe before running in a hat-trick in a 29-12 victory over France.
England also registered a 19-12 win against Kenya but their 'prize' for topping Pool C is a clash with reigning HSBC World Series champions New Zealand, who were beaten 21-5 by South Africa.
England coach Ben Ryan said: "We have played New Zealand here twice in the last five years in the knockout stages and luckily we've come out on top.
"They have never lost two games in a row in the World Series and Gordon (Tietjens, their coach) will be hurting from what was a fairly emphatic victory for South Africa.
"I am sure they will not have another poor display like that and I expect a gold standard performance from them tomorrow."
Wales had already booked their quarter-final place with a 14-7 win against Scotland and a 15-12 triumph over Canada when they produced one of the performances of the day to beat Australia 33-14.
Wales trailed 14-12 at the interval but hit back with 21 unanswered points, including two tries from Richard Smith.
"I thought the boys were outstanding in that last tie," Wales coach Paul John said.
"We knew that it would be a tough pool. We had a dog fight with Scotland. They're a very good side. People don't realise how good they are.
"Canada beat us the last time we played them and they've just won the Pan-Am games. Thankfully we managed to get through those first two games and that guaranteed us a place in the Cup quarters.
"We were able to relax and show what we could do against Australia."
South Africa will face France and Fiji tackle Australia in the other two cup quarter-finals.
Scotland beat Canada 19-14 but lost 24-12 to Australia and dropped into the bowl competition, where they will face the United Arab Emirates in the quarter-finals.
England's women booked a semi-final clash with Australia in the inaugural IRB Women's Sevens Challenge Cup with victories over China (26-15), South Africa (22-19) and the United States (31-0).
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