The therapy - which is particularly helpful for children with rare and complex tumours - was highlighted with the case of Ashya King last year.
The five-year old's parents took him abroad after doctors in the UK did not recommend it for his brain tumour.
Experts say the new centres will be "game-changing".
The therapy allows precise targeting of certain tumours, increasing the success rates and reducing the risk of damage to surrounding tissues.
But it is not yet available in the UK - apart from one clinic to treat eye conditions.
On Wednesday, a ceremony at University College London Hospital (UCLH) - attended by Health Secretary Jeremy Hunt - marked the start of construction at one of the sites, due to open in 2019.
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