The win saw the 23-year-old Pole notching her 12th successive victory in 2013.
"There is," she said when asked if 13 was considered an unlucky number in Poland as she looked ahead to her fourth round clash with Serbian 13th seed Ana Ivanovic.
"I didn't say that," she hastily added with a beaming smile as if to banish any potential misfortune she may have brought upon herself.
The world number four, who could also win her 13th career title if she goes on to lift the Daphne Akhurst Memorial Trophy, was also quick to point out that she was "not actually" superstitious.
Radwanska, who won the Auckland and Sydney titles before the Australian Open and said earlier she "hoped" she was not in the form of her life, added she could not think of a better run of victories and felt she was building nicely into the tournament.
"I think it was a good start," she said of her pre-Australian Open preparations. "Well, I can't complain.
"I really had a lot of good matches against top players this year, and I must say I'm really playing good and everything is working.
"I just hope I keep going. Of course now is gonna be harder and harder playing against seeded players."
Radwanska had little trouble against the 20-year-old Briton, taking advantage of cooler conditions in Melbourne to continue her red-hot start to the year.
Temperatures had exceeded 40 Celsius (104F) at Melbourne Park on Thursday but a cool front pushed through early on Friday, bringing rain showers that forced a slight delay to the match as the roof was closed on Hisense Arena.
The 23-year-old, who took a medical timeout after the first set to receive treatment for a cut finger, however, was not slowed by the delay and romped to the win in 84 minutes.
"I think I was really solid from the beginning, trying to be focused," she said.
"Especially in the beginning of the first set I was really tight, and I think that game when I was serving when it was 2-1 (to Watson), I think it was really important game.
"I think then I start to play better, and of course in the second set I was trying to, you know, to start good as well and not to lose my focus."
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