Mum is correct
Putting the car in dads name does not alter the fact that you will be the main driver and so it is still illegal as that is what makes it "Fronting"

You are not going to get cheaper than £4000

As an example On 03/03/2011 I got a fictitious quote from a well known comparison site on the following ..... Mr Smith, 17, passed test 4 weeks ago, full time shop assistant, Vaux Corsa 1.0 litre worth £2000 not modified registered in 2003, parked in a driveway at night, used for social and commute to one workplace and no restrictions on when it could be driven, policy excess £550 total, 10000 miles a year living in a lowest possible car crime risk postcode. A very simple case which should bring close to the best possible and typical price at 17.
Result - from 121 insurers only 31 quoted. Cheapest was £4800 a year or £747 deposit and £524/month for 9 months (highest for same cover - £8004/year)

Realistically in today's economic situation with insurance prices the way they are you are too young to contemplate running a car. Looks like that is the way it is now for younger potential drivers. At various times as you go through life there will be things you would like to be able to do or have but due to age and/or finances you cannot - for many teens this is how it is now for cars in that just like me and a new Ferrari I don't have enough money.

Even if your Dad registers the car in his name, when he insures it he will be breaking the law by saying that he is the main driver when in fact the main driver will be you, your Mother is right it is called fronting and the insurance companies and the Police are well aware of it, insurances will check to see what other motor insurances he has and they will see that he is also the main driver of his own car, a person is not generally the main driver for more than one car and the alarm bells will start ringing, I feel very sorry for young people, car insurance is overly expensive compared to when I was young, I have included a website that shows a number of cars in group 1 (cheapest) this is for new cars but I assume that older versions of the same cars are still the cheapest.
Addition.
Emmo, I have never heard of this before but it is a brilliant idea, I hope that it does not end up on all cars though, it sounds a bit like big brother has arrived and is checking up on us all but for young drivers, it would be a great way of separating the good safe drivers from the bad dangerous ones.