My hybrid bike tire measurement says 700x35c. I ordered a replacement inner tube stating it was 700x35-40c but when it arrived it is actually 700x38-45c. Could I still use this or will it cause a problem, e.g. with my brakes?
It won't cause a problem with your brakes – the tire casing will prevent the tube from "over expanding."
Your tire is a bit smaller than the small end of the range for the tube. You may find it a little harder to fit in the extra material and it would be good to take a bit of extra care to make sure you don't pinch the tube if you use tire levers.
Be careful to avoid any twists, but it should work. This question, Using a wider inner tube, explains in more detail what can go wrong if the tube is significantly too large, and also points out that inflating the tube slightly will ease installation – especially in a case like this.