Basically, what I'm looking for is this: ieGeek® ORVIBO Smart Wall Socket but without a proprietary app. I just want something open and "general purpose" like with a REST API interface to pilot it with my RPi (e.g. with a Python script), without the need to hack it.
You would need to buy a 5 V relay board like this one:
It connects straight to your GPIO pins and it is easy to find scripts and even phone apps that run it as it works by just switching the GPIO pin to HIGH.
The boards come in many sizes and you would just need to wire one live wire through and it will act as an electronic switch you can control with your pi.
Just make sure to check that its voltage rating is high enough as this changes between countries.
Perhaps then this is something that would solve your problem: 2 Channel USB/Wireless 5V Relay Module
As it can work over Wi-Fi you could use your Raspberry to control multiple relays across your Wi-Fi range and is installed in the same way you are used to.