They are believed to be largely household clusters linked to people who travelled from India.
"There were 17 cases of the Indian variant in Wales yesterday and over 700 in England", he said.
Boris Johnson has admitted the government is "anxious" about the growth of cases of the variant in the United Kingdom, which rose from 520 to 1,313 this week.
The Prime Minister has said there is "increasing concern" about the variant and warned the emergence of further new variants "pose a potentially lethal danger".
Is the B16172 variant driving the second wave in India?
Professor Steven Riley, from Imperial College London, said that whether the road map for England continues on its planned trajectory was "a Government decision" but suggested the United Kingdom was now in a good place, although variants were being watched.
Scientists are keeping a close eye on the spread of the variant across the United Kingdom, with a big rise in cases expected to be revealed on Thursday.
Public Health England has recorded 1,313 United Kingdom cases of the Indian variant in total, with nearly half of these cases related to travel or contact with a traveller.
Greater Manchester Mayor Andy Burnham has submitted a request to the Joint Committee on Vaccination and Immunisation that all over-16s in Bolton, along with the rest of the Greater Manchester area, are able to receive a Covid-19 vaccination "to mitigate the risks of spread in those communities where we are seeing more transmission".
Public Health England is working with the health system and borough councils in parts of the city where cases have been identified. Anyone who visited the venue on Front Street between 23 April and 3 May is asked to "immediately" book a PCR test.
How many cases have been detected in the UK?
Surge testing is already taking place in 15 areas across England with increased testing and enhanced contact tracing attempting to prevent the spread of outbreaks.
He told the PA news agency: "B16172 seems to be slightly more transmissible and capable of outcompeting the B117 or B1351 (South African variant) to become the dominant variant in the UK".
The React study looked at variants of coronavirus and found that of 115 positive swabs, 24 cases were identified as the Kent variant, and two of three cases in London were identified as the Indian variant of concern.
Health experts said they "haven't seen any hint" of a current Covid variant that can fully evade the effectiveness of vaccines.
However, the European Medicines Agency said on Wednesday it was "pretty confident" that vaccines now in use are effective against the Indian variant - a view echoed by some British scientists.
He told BBC Radio 4's Today programme, "The vaccines don't 100% prevent infection for people".
"And we actually see that difference growing nicely now for hospitalisations as well, so for each infection in the community we are producing fewer hospitalisations and far fewer deaths".
"The top-line government policy is driven by protecting the NHS, so even if infection starts to go up, we then need to assess whether that's bringing a lot of new cases into hospitals, and there's certainly no sign of that at the moment".
Could the variant delay lockdown ending?
Paul Hunter, professor in medicine at the University of East Anglia, said the 21 June lockdown lifting in England is in doubt, particularly if the Indian variant causes increases in cases in elderly people and a rise in people needing hospital care.
Johnson was asked if local lockdowns were possible, he said, "There are a range of things we could do, we want to make sure we grip it".