Boris Johnson has been kept “regularly informed” on the flooding situation, the environment secretary said during a visit to flood-hit Shropshire.
George Eustice, who was in Ironbridge and Shrewsbury earlier, said the prime minister “made it clear he wanted me to lead on this”.
It follows criticism of Mr Johnson for not visiting flood-affected areas.
Mr Eustice also said £4bn would be spent on flood defences over five years. The money was pledged last year.
Storm Jorge, due to hit at the weekend, could bring more disruption to the region, with heavy rain also forecast on Friday.
As well as the flooding in Shropshire, up to 70 properties in Snaith, East Yorkshire, have been flooded.
During his visit to Ironbridge, Mr Eustice said: “The prime minister when he appointed me two weeks ago made it clear he wanted me to lead on this.
“We discussed Storm Dennis that was coming that weekend… discussed our response.
“I’ve kept him regularly informed with what’s happening; the important thing is have we made the right decisions in a timely way? And I think the answer is yes.”
Mr Eustice praised the teams working “on the ground”, who have done a “fantastic job at responding to this” and said the government would look to make improvements to defences, some of which buckled in Ironbridge on Wednesday.
“We’ll be spending over £4bn in the next five years on flood defences,” he said.
The money was pledged by the Conservatives in their manifesto ahead of the 2019 general election.
“Some of that is going to be on nature-based solutions upstream to try to hold water uphill so vulnerable communities like this on the Severn are less likely to be affected, but there will also be some hard defences put in place as well,” Mr Eustace said.
He refused to be drawn on exactly which projects would be backed, saying there would be assessments based on flood risk and the total of number of homes potentially protected.
Steven Clarke, who runs an allotment in Coleham, Shrewsbury, said it was an “insult” Mr Eustice did not speak to residents and business-owners affected by recent flooding.
“We were promised we would be able to speak with him and that was the purpose of his visit,” Mr Clarke said.
“We were quite keen to speak to him and get some answers… he walked straight past and went towards the bridge to go and do some press interviews.”
On Wednesday evening, police and the Environment Agency warned of “another 10 days of difficult conditions” over fears Shropshire and Worcestershire, where evacuations have been taking place, will be further affected following heavy rain in Wales.
The Met Office warned parts of Wales and northern England could see between 60 to 80mm of rain on Friday – with much of the rainfall in Wales falling into the Severn catchment and heading towards flood-hit communities in the West Midlands.
There has been some respite, though, with river levels recently dropping by about 40cm in Ironbridge and by 80cm in Shrewsbury.
Rachel Moss, who has a hairdressing salon in Coleham, said people “need some action”.
“We’ve been hit twice in a week – there’s still rumours it could get worse this weekend,” she said.
“If it does, it will absolutely devastate this community.”
Chris Bainger, from the Environment Agency, said: “We have a bit of respite, we’ve just got showers moving through over the next couple of days.
“But coming into Friday we have another band of rain coming through that’s going to be up in the Welsh mountains and that’s going to be coming to us… perhaps Saturday.
“We’ve already planned another 10 days of being on 24/7 manning of our incident rooms and having operational staff at all of our barriers.”
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