In addition, MEPs in the European Parliament will be signing a giant Valentine's Day card saying 'Stop Burberry breaking our hearts'.
Union organiser Mervyn Burnett said: 'GMB's campaign takes on a global dimension, which follows Burberry's own globalisation moves. Members and supporters will explain direct to shoppers outside the Burberry stores in these cities GMB's demand that the company reverse the closure of the South Wales factory.'
A source close to the upmarket fashion brand said the company is 'very concerned' about the effect of today's demonstrations.
Burberry had to withdraw its sponsorship of a pre-Bafta party recently because of protests over the factory's closure. Workers had planned to picket the 800-guest party.
Burberry is closing its factory in Treorchy to relocate production overseas, with a loss of more than 300 jobs.