The only available option that I could find was OwnFone

It's a customized phone that is made specially for the customer based on their order. They company intention is to provide our elders with an emergency easy to use phone however, it can be used a for children as well
- Buttons can be images (or names) in case you child is too young to read
- 999/emergency button is available
- No text, no screen
- Choices of 2, 4, 8 or 12 pre-programmed numbers depending on how much you willing to pay
- Designed and works only in the UK
Biggest downside is that the phone is not SIM-free and it seems you cant even replace the SIM or the battery so you are stuck with the plans offered to you by the company.
The cell phone can be bought from this website
Edit: It's available for children now from Mobile phones for children