Thank you for your comment. :)) That's a good point, which I did not consider. After doing a bit of reading, it seems that the P.1 strain only appeared in the U.K. recently - 6 such cases as of March 2021.
https://www.theguardian.com/world/2021/mar/01/brazil-covid-variant-p1-britain
But apparently, the South African strain was detected in the U.K. since December 2020 - 105 cases so far as of mid-February.
So, yes, the detected cases in this study may not belong to the U.K. strain completely. I checked back the study methods and they mentioned that the S gene negative result is "highly likely" to be the U.K. strain. I think I've to insert an update at the end of the article about this. Thank you, again, for pointing this out.