Note: I asked HESA if they broke the data down further, and delineated undergraduate vs postgraduate numbers & percentages for non-EU domicile students. Their response included the following:
HESA finance data does not distinguish between undergraduate and postgraduate tuition fee income for non-EU students.
The HESA student data does show the numbers of non-EU students by level of study. Please see the fourth table in this release for a simple breakdown of student numbers by domicile and level: http://www.hesa.ac.uk/pr172 .
Table 1 from this release has this data for the last five years: http://www.hesa.ac.uk/sfr169 
The ‘Students by Institution’ table from this page has the same data broken down by institution: http://www.hesa.ac.uk/content/view/1973/