Yes, you can bring them, but they are considered "used animal equipment" and must be declared at the border for inspection:
You must declare certain food, plant material and animal products.
Live animals and animal products:
- used animal equipment including veterinary equipment and medicines, shearing or meat trade tools, saddlery and tack and animal or bird
Collars and leads should be fine, but the bed may be a bit iffy if it has hair etc, so you'll want to clean/wash it thoroughly first. The customs officer will decide. Even the worst case is just confiscation: you will not be penalized otherwise as long as you have declared them.