Haast Sergeant Mark Kirkwood, who is in charge of the search and rescue, said Ms Simpson was "reasonably experienced and very fit", the overnight temperatures have not been very cold and the rivers were not as high as they have been recently.
The 32-year-old from Essex is believed to have gone for a hike over the weekend, but was reported missing around 8:45am yesterday when she failed to keep an appointment.
Sgt Kirkwood said she was on a day hike to Mt Brewster Hut and had planned to walk up to the glacier about 2km north of the hut. She also planned to visit Blue Pools, near Makarora.
She was carrying a day pack and did not take a search and rescue beacon with her.
He said there were currently three search and rescue teams on the ground and another was on the way from Westport and expected to join the search shortly.
A Wanaka team was walking in from Makarora towards the route by Mt Kaye, a Wanaka Landsar team was walking from Fantail Falls up to Mt Brewster hut and a Fox Alpine Cliff rescue team was walking from Mt Armstrong towards Brewster glacier and they also have a search dog with them, he said.
Members of the public were at the Fantail Falls car park from 7.15am waiting to join the search and others have been calling in throughout the day.
Meanwhile, Ms Simpson's family are desperate for news from the foot search under way today.
Friends earlier told the New Zealand Herald they had not heard from her since Friday, and her family were "really hoping" for news, a spokesperson said today.
"Until they get some news, [the family] are in the dark. Just really hoping we may hear something today from the foot searches," the spokesperson said.
Ms Simpson arrived in Wanaka in November and has been working as a landscape gardener for Doug the Gardener.
Her family were very concerned but were keeping their fingers crossed for good news today as the search progressed.
"It's hard not to think the worst but they are trying to stay positive. Hopefully, she just needs a helping hand to get out."
A close friend told the New Zealand Herald it would have just been "another weekend away tramping" for Simpson.
"She's strong, she's fit, she's capable. She's worked in the outdoors, she knows what she's up to."
She said Ms Simpson arrived from Australia last year alone and has been living in Wanaka since July.
The friend, who didn't want to be named, described the Brit as "outdoorsy, super friendly and super bubbly", and said she would explore the area as much as possible.
"She's a really beautiful, kind-hearted person. She can make friends in an instant, she's awesome. She's just here to tramp and see the country."
The friend hoped she would turn up soon.
"It wouldn't surprise me if she did just rock up tonight and there's been a little something that's happened and she just needed to take an extra day," she said.
A state of emergency was declared in flooded Southland, where roads were closed and a steady downpour left homes and farms sodden.
The swollen rivers may have also been responsible for the deaths of two trampers who got into trouble while heading into the Mt Aspiring National Park.
Senior Sergeant Miriam Reddington said their bodies were found in the Makarora River, near the start of the Blue-Young link walking track and just upstream of the confluence of the Young River.
''All our inquiries indicate they were going for a hike.''
One body was recovered on Friday afternoon by the Wanaka Search and Rescue river rescue team, and the second on Saturday.
Reddington said police were trying to establish when the trampers had left.
The deaths were not considered suspicious, and police were not looking for anyone else in connection with the incident, she said.
''We think they have just come unstuck.''
Reddington said police were working with the Department of Conservation to make sure it was safe for trampers to continue using the area.
Central Otago District operations manager Mike Tubbs said the Makarora River fluctuated ''wildly'' as a result of rainfall and snow melt and the nearest river level monitoring site showed the Wilkin River, which runs into the Makarora, went from 300cumecs (cubic metres per second) to 900cumecs and back to under 100cumecs in the space of four days last week."
The steep walk to Brewster Hut can take up to four hours one-way and is recommended for experienced trampers only.
Trampers cross the Haast River and are advised to exercise caution after heavy rainfall.
MetService meteorologist Tuporo Marsters said the heavy rain that overwhelmed Southland would have begun to recede by the weekend and it was unlikely the Haast River would have still been in flood.
- additional reporting RNZ/NZ Herald
