Latest figures show there are 1,313 cases of the variant in the UK, up from the 520 recorded the previous week.
But vaccines minister Nadhim Zahawi said the COVID-19 roadmap for Monday “remains in place because the vaccines are delivering”.
“At the moment we have no evidence that it escapes the vaccines or is more severe in its impact on people,” he said.
From 17 May, pubs and restaurants will be able to reopen indoors and people will be allowed to mix indoors as two households or under the rule of six.
People will also have the choice whether to socially distance with close family and friends they meet up with.
On 21 June, step four, the government wants to end “all limits on social contact”.
Asked about this step, Mr Zahawi was more equivocal, saying that ministers would monitor the situation with the virus and be “guided by the data”.
Meanwhile, Wales First Minister Mark Drakeford has told Sky News that the Indian variant has delayed the lifting of some restrictions there.
Wales will move to alert level two on Monday, with the reopening of indoor hospitality and entertainment venues.
However, Mr Drakeford said the variant has “already impacted plans” causing them to pause some easements they were going to introduce on Monday.
These included reopening smaller events and relaxing the rules for mixing beyond extended households.
“There were 17 cases of the Indian variant in Wales yesterday and over 700 in England,” he said.