Things you can look into which helped me, adding parents on as secondary drivers (if they have high no claims, no points or low points etc),
Once you get a quote you think is reasonable, phone them up and see if you can get lower. I managed to get elephant, from 700 to 540 by doing 10months insurance but get a year NCB for it. And spoke about paying 540 over 2 months instead of paying 800 over the whole year in monthly installments.