I ordered a Logitech keyboard and mouse separately since I didn't find a combo that I liked with UK layout (I'm in Finland). Will I need to plug both the receivers in the USB ports or can both keyboard and mouse use just one receiver? Thanks
... if, and only if, both of the devices ship with a Unified receiver you can program one of the receivers to communicate with both devices. You would need to download the appropriate utility software from Logitech's website. Until you reprogram one of the recievers you will need to connect both. If either or both devices use a plain receiver you will have to connect both receivers. Only the Unifying receivers support multiple devices.
As long as both devices support the unifying receiver (denoted by the orange 'flower' icon) you can then use the Logitech Unifying Software to pair both devices to one Unifying Receiver.
I currently have two Unifying Receivers, an MX Master (keyboard) and an MX Keys (mouse). I have one Unifying Receiver plugged into my work PC, and another plugged into my Mac mini. Both receivers have the keyboard and mouse paired to them, so I can switch them both between my PC and Mac, using up only one USB port on each.