I currently have the following positions available:
(1) Prestigious PhD scholarships for high-performing students
UK research councils general require PhD students to already have a masters degree, unless it is a 1+3 year studentship, which includes a masters degree during the first year. However, these studentships generally apply only to UK students or EU students who have been in the UK for at least 3 years prior to start of PhD. The latter are, e.g., EU students who already did their undergraduate studies in the UK. An exception is when the student is self-funded, and so the studentship can at least be used to pay university fees.
In contrast to the UK research council funded studentships, there are two prestigious scholarships provided by Imperial College, who allow very talented students to bypass the above mentioned restrictions. In particular, they can be used by overseas students or students who do not have a masters degree but are good enough to go directly to the PhD. Please see following links for application details.