My daughter just applied normally through UCAS (this wasn't for medicine though) and then Notts admissions forwarded her application to elite sport to look at. They asked her some questions about grade predications, GCSEs etc... to check she would get on her course and of course some information about her sporting achievements.
She had mentioned her sport in her personal statement, so I think Notts admissions picked it up from there. There is an expression of interest form on the sports scholarship page though too. I think she did that as well.
She had been selected to compete for England U20s that summer, and was ranked in the top 5. Its higher now, but at the time of her UCAS application that was where she was at.
They then invited her after she'd had an offer to apply for a sports scholarship, not heard on that yet as the closing date was only Friday.