The chemist has denied the claims, saying they are "simply not true" because "the number is based on inaccurate and theoretical calculations."
But this afternoon anti-tax avoidance group UK Uncut said hundreds of people were demonstrating outside Boots shops in Liverpool, Manchester, Northampton, Ashford, Penarth, and in Victoria Street, London. They added that campaigners would be moving to a "secret location" later today for more protests.
Campaigners are currently setting up camp outside Westminster Abbey.
Jo Hill, UK Uncut's spokesman, said: "Boots get 40% of their revenue from contracts with the NHS, funded by taxpayers, yet they think it's acceptable to not pay taxes themselves.
"The tax dodged by Boots could pay for the starting salary of more than 78,000 NHS nurses for a year - that's roughly 120 additional nurses per parliamentary constituency. The Government should stop tax avoidance and stop cutting our vital public services."
Charley Dainty, a football coach at the Victoria Street protest, said she was there to vent her "anger" at big companies dodging tax.
She continued: "I want to send a message to a government who is doing nothing about it. I'm sick of hearing that we cannot afford to pay for our NHS or that we need to cut our public services while the rich are allowed to keep on avoiding tax."
Demonstrators used the Twitter hashtag #BootOutBoots to post updates, including photos of wheelchair users chaining themselves to railings and tweets about police officers allegedly searching their bags and phones.
But a Scotland Yard spokesman said police "were not aware" of any demonstrations connected to Boots.
He added: "On any given day there are about five protests going on in central London. We can't give time to all of them, but we do react if there's a need."
A spokeswoman for Alliance Boots said: "The claim that Boots have avoided £1.2 billion in tax is simply not true.
"This is based on the assumption that any company carrying corporate debt is practising tax avoidance.
"All companies, large or small, that carry debt are afforded tax deductibility of their debt interest in the UK.
"If we look at the real numbers, our corporation tax increased by 40% last year compared to the previous year - from £64 million in 2012/13 up to £90 million in 2013/14.
"Looking after many millions of customers for their health and beauty needs, we invest significant amounts in the UK, around £1.2 billion since 2006, to further develop our stores and services so we can serve people in the best possible manner."