Tesco's eBay Outlet store is selling the Injusa Flames Quad Bike for £39.99 with free delivery.
A very similar quadbike - different flames, but the rest seems the same - on Amazon is currently £69.99, so this seems like a fabulous price.
The quadbike comes with a rechargeable 6V battery and charger. It has a robust plastic frame and a foot pedal accelerator with an automatic rear brake. It goes up to 3mph, which means you can have a stroll alongside it.
The maximum user weight is 20kg, so it really is only for little ones, and the maximum speed is low enough that they won't get too far without you.
I'm not sure this one will fit under the tree, but since it requires some assembly, you may want to set it up in another room!