Will the insurer check all the details of my application for car insurance? If not I might be able to hide the fact that I have had three accidents, all my fault, in the last year.

In fact the insurer may not check the accuracy of the information you give, but it may mean that when you make a claim it will be refused. In other words, there is every possibility that the information will be checked at the time you make a claim, and therefore a serious possibility that payment will be legally rejected.