The MSc Statistics (Research) and MSc Statistics (Financial Statistics) (Research) programmes are eligible for ESRC '1+3' funding. The MSc qualifies as the first year of doctoral training (the `1'), followed by the MPhil/PhD Statistics programme (the `3').
ESRC studentships are available to UK and EU students. They cover full fees (UK and EU level) and an annual stipend, which for 2017 was £18,000. Further details on eligibility - http://www.lse.ac.uk/intranet/students/moneyMatters/financialSupport/ScholarshipsLSE/PhDApp/MResMPhilPhDProgrammes.aspx
Potential applicants should contact the Department at email@example.com in the first instance to express their interest. Applicants should then complete an online application for their chosen MSc (Research) programme, including an outline research proposal, and specifying that they wish to be considered for ESRC 1+3 funding. Note that applications are now closed and will open in Autumn 2017 for entry in 2018-19.
Further details- http://www.lse.ac.uk/intranet/students/moneyMatters/financialSupport/esrc.aspx