There are now many insurance companies who will deal direct with customers, whereas in the past it was all done through brokers or other third parties. But to go to all the different automobile insurance companies for quotes yourself would be very tedious and time-consuming.
If you have access to the internet there are now many sites that will take your details and submit them to a number of different companies to compare and deliver quotes on your behalf. If you do not have access to the internet, there are telephone services as well, which can be found in the Yellow Pages. There are also independent insurance brokers, some with high street offices, who will search around for a quote on your behalf.
The thing to be careful with, regardless of how you shop around, is that you must be aware of the details of what's included in each policy. One policy may have a cheaper premium but not have, for example, legal assistance included in the price, so another, initially more expensive quote that has legal assistance built-in, may be cheaper if you want that. So although you can shop around easily, make sure you understand the details before you commit.