The variant, VUI-21MAY-01, has been designated as a Variant Under Investigation by PHE, and was discovered by a team at Sheffield University and Sheffield Teaching Hospitals.
There have been 49 cases across the country to date - the team in Sheffield are currently sequencing other positive tests from hospitals in the region to ensure local teams have up-to-date information on the virus.
There is currently no evidence that this variant causes more severe disease or renders the vaccines currently deployed any less effective.
Sheffield's Director of Public Health, Greg Fell, said: "Please don't be alarmed, we want you to continue doing what you have been for the past year. Follow the guidance, continue to wash your hands regularly and wear a mask indoors."
A statement by the group in Sheffield said: "The recent B.1.1.482 samples from South Yorkshire described here have acquired a significant number of mutations when compared to other SARS-CoV-2 viruses of the same lineage."
It adds: "Because of the number of spike gene mutations also found in variants of interest or concern or under investigation (VOC or VUI), we recommended that this lineage is monitored closely for possible increased community transmission and functional studies undertaken to understand the impact on antibody recognition."
Analysis by ITV News' Science Editor Tom Clarke
To put this into context there are currently 13 variants of coronavirus under investigation by Public Health England - only a couple of those, the variant from South Africa and the variant from India have required surge testing.
One of the tools they are using to track these variants is that they look slightly different on the PCR tests that they use for screening people who have covid. So the more new variants that pop up on the scene can slightly cloud surge testing in other areas. But we are really good in the UK at sequencing new variants of the virus.
We are seeing more mutations of the virus quite rapidly as it gets into more people, so it is inevitable we will see more of these, but most will not amount to much.
Increased laboratory testing is being carried out to better understand the impact of the mutations on the behaviour of the virus.
PHE has said that all appropriate public health interventions are being undertaken, including additional contact tracing and targeted testing.
Where cases have been identified, additional follow-up of cases, testing of contacts and targeted case finding will limit the spread of variants.
Dr Kevin Smith from Public Health England said that people shouldn't be overly worried, but that people should continue to follow social distancing, handwashing and mask-wearing guidance.
He said: "We have identified a cluster of cases, mostly in Yorkshire, that have a series of mutations which is unusual and we are keeping an eye on that."
He added that there is currently no evidence that the mutations make the virus anymore transmissible.
The Prime Minister's official spokesman said: "There have been a number of variants throughout the pandemic and there will continue to be so.
"There are three mutations of the B1617 (Indian) strain, as I think has been discussed previously, but as we do with all variants where we spot and identify them through our genomic sequencing programme, we will continue to monitor them and we will designate them as variants under investigation, and then variants of concern if we deem them to be of greater risk."