UKIP has emerged as a major force in British politics in recent years with its anti-European Union and anti-immigration posture. It is widely expected to upset calculations in the 2015 elections of the three major parties: Conservative, Labour and Liberal Democrats.
Thandi, 21, had earlier defended the party strongly in television debates, but UKIP's recent poster campaign ahead of the May 22 elections to the European Parliament upset her, particularly one that suggests 26 million people in Europe were after British jobs.
Announcing her resignation, Thandi wrote: "The poster epitomises where the party is going wrong. This anti-immigrant campaign undermines UKIP's claim not to be a racist party. They are turning the election into a game of 'us' and 'them'. Well, I am with 'them'."
She added: "I understand that British politics in the 21st Century has become a dirty game of populism, but UKIP is straying further and further from the policies that attracted so many of its original supporters, instead cynically pursuing ever more aggressive anti-immigrant rhetoric."
Thandi, who joined the party at the aged 17, is also the Fashion Editor of The Beaver, a weekly of the LSE students union.
UKIP described her resignation as "of no great significance".