When I was looking for a cheap car, I always checked insurance before buying.
A lot of my friends didn't and they weren't very happy they were paying through the roof for insurance.
I was looking a cars ~£800 - £1000, but by paying up an extra £100 here or there on the car could reduce the insurance by more than that.
In general for low insurance
Small engine, small car.
Also look at ways to get insurance cheaper (without fronting).
The easiest way to do this is add as many people you know (in reason) who are experienced to the policy.
I added my parants and my sister to my first one, which brought the insurance down by ~£500
The cheapest insurance cars are usually more obscure cars or what would be considered "old people" cars. I had a 05 Picanto as my first. Car cost £800, insurance was about the same for the year.
In general, Corsas and Fiat 500s which you see everyday can be "reasonable" for insurance, but because the only people who really own them are <25, then that will mean the premiums will be higher.
For cheap cars, just go on gumtree and use the filters to put in your requirements and budget and just see what comes up.
Really depends on what you mean by reasonably inexpensive though.
Rule of thumb though is insurance on cheap cars will be roughly the same price as the car itself. If not more.