Rhodes recipients attend an Oxford college in England, but you need to research which college and program to puruse. Therefore you would need to do more extensive research on the programs available at the various British universities. A catalog describing the numerous programs is available in the Honors Program Office. It is similar to the Rhodes and Marshall, except the age limit is 30 and it is used at Cambridge University in England only. Please check the web site for specifics about eligibility and the application process.
Deadlines vary according to program.