But some fans were unimpressed by the jibe, with one tweeting: 'Wait the interviewer told Taylor to take a shower??? wtf'.
Another wrote: 'Really Greg James? The first interview Taylor has done in more than two years and you tell her she needs a shower?
'Really where did your manners go? And you couldn't have asked her a music question about her album? Is this journalism?'
However, some fans managed to see the funny side, calling their awkward exchange 'TV gold' while others labelled it 'classic British humour'.
One penned: 'People need to stop creating problems, the whole Greg James shower comment was a joke, it was crazy humid today, plus performing, Taylor didn't even take offence.'
Another wrote: 'Taylor and Greg James have done interviews and stuff before and she obviously wasn't taken aback or offended by his joke can ya'll relax.'
Moments earlier, Taylor, 28, had wowed the 26,000-strong audience with a live performance of a string of hits from her 2017 album Reputation.
The star admitted to feeling 'a bit nervous' before her performance, telling Greg: 'We pretty much had no time to rehearse for this. This was kind of like, on the fly.'