Where can I find (preferably UK) statistics about where graduate students did their undergraduate course?
The Higher Education Statistics Agency would be your first port of call in the UK.

HESA collects statistics from students across HE institutions and publishes their results.  It is my understanding that all UK HEIs are required to submit data about their students, so coverage should be relatively complete.

Most of the attention is generally paid to what students do 6 months after that have graduated from an undergraduate courses; however, their data appears to be available, so you might be able to do your own analysis looking at graduate destinations>further study>subject studied.  See 'free online tables' on the Graduate Destinations page.

You might need to speak with HESA directly to drill down to institutional level.  They have advice for data analysis as well, so maybe worth getting in touch.