We had much the same with my 17 year old daughter, in a 1.4 Punto Sporting.
Insured in my name with her as a named driver - £5000
Insured in her name alone - £3500
Insured in her name with me as a named driver - £1300
Insured in her name, (as above) plus my 74 year old father as a named drivers - £1100
Insured in her name (as above) with a little black box fitted on Admiral multicar - £850.
I even tried substituting my father for my brother, next door neighbor etc, which made no difference.
Removing my father/brother/neighbor and adding the wife instead, it went up by about £50.
12 months later her renewal was down to about £590,
It pays to tinker with the figures.