With Apple, Apple does not repair or replace the Home Button of the iPhone 4, they only offer replacement iPhone 4 exactly like yours. If you have Warranty or AppleCare it will be covered. If no coverage the cost is £ 126.44
If you want you can use Assistive Touch in Settings App for perfect Virtual Home Button. Settings App > General > Accessibility > Assistive Touch > ON > tap the new white screen button > Tap Home.