The Department of Statistics pays for up to two bursaries per year. They may not be awarded if there aren't any strong enough applications, so it's a tough one to get. They pay for full academic fees, and a stipend of 14,140 Pound Sterling per annum. The bursaries are awarded for one year, and may be extended up to two more years.
In order to be eligible for this award, the student must have been ordinarily resident in the UK for at least three years and this must not have been solely for educational purposes (unless the student is a EU national). Furthermore, the student must have permission to reside permanently in the UK.