LONDON (Reuters) - The number of non-EU students coming to Britain jumped by a third to more than 300,000 last year, prompting the government to order a shake-up of the visa system which it said was open to significant abuse. Home Office figures on Monday showed the number of students increased by more than 75,000 in the year to March to 313,000. The influx was exacerbated by students bringing with them 31,000 dependants, the department said. That compared with 235,000 students and 25,000 dependants in the previous year.