I've just spoken to my friendly local independent insurance brokers to see if there's some way around this, if there is, they are not aware of it, because you need to have an actual car before getting insurance on it. I did ask if you could take out insurance on a car owned by a family member or mate, and switch it to a different car when you buy one, but that's a no-no, because most insurers will only offer cover to the owner of the car, plus they would see a policy was already in place on the national motor insurance database.
He did say that not all insurance companies have big hikes if you buy right at the last moment, so it'll be best to shop around at the time and hope for the best, he also said that they are not very competitive when he comes to younger drivers, but they should be with older drivers, even if they have only just passed their test.
I would suggest, as well as using the comparison sites, it would probably be a good idea to try a decent local independent broker, or even my broker, I'll be happy to PM you their number if you want.
Of course there's no guarantee that a broker will come up with the best deal, but they do tend to be aware of more specialist insurers, that are less likely to be on the comparison websites. They did sort me out with one specialist insurer for an unoccupied property, which a lot of insurers are not interested in quoting on.
Getting temp insurance is an option, but it tends to be bloody expensive, and would be pointless if it costs more than any saving on getting standard insurance 3-4 weeks in advance.
Beyond that, I guess the only option would be if you had some secured off-road parking option, where it could sit for a few weeks, before the insurance came into force, but then that would be a proper pain, as when you pass the test, you want to start driving straight away.
