The machine was being given away attached to the cover of MagPi magazine.
The Raspberry Pi Foundation, which manufacturers the Zero said that it made 20,000 individal Zerps, with 10,000 more being given away free on the magazine.
The machine, which has a 1GHz ARM chip and half a gigabyte of memory. It uses a flavour of Linux, Raspbian, as it operating system and also comes with two USB ports, an SD slot, and a HDMI slot.
The magazine is being reported as sold out all across the country, but the Foundation said there are still copies out there. One person claimed that some individuals were going into WH Smith and other outlets and buying up all the copies that were in the shop.
Some people have started selling copies of the magazine with the free Zero on Ebay. One is being sold for £79 – see screen capture above.