Botany was a branch of biology dealing with plants. It was studied by Peri Brown before leaving with the Sixth Doctor; (TV: Timelash, The Mysterious Planet et al.) the Doctor defined her "a bit of botanist". (TV: Timelash)
George Cranleigh was a famous botanist. Amy Johnson wrote A Textbook of Botany for Students, a book the Fifth Doctor came across while exploring Cranleigh Hall. (TV: Black Orchid)
Lord Ravensworth described himself as an "amateur botanist" and owned a book on botany. (TV: The Mark of the Rani)
The Tenth Doctor claimed that he always got top marks for botany at school. (PROSE: Wooden Heart)
According to Supergirl, E.T. had a phone which could get 'crazy coverage', and he could 'even call his crew of intergalactic botanists'. After she stated this, E.T. grew a Kryptonian singing flower for her. (WC: Supergirl Meets E.T.)
Torchwood had botanical records going back 100 years. Torchwood Three's Hub contained a Hothouse, which contained plant specimens from different planets and time zones to 21st century Earth. (PROSE: Plant Life)