Not sure about UK products, but you can look the ones on this list http://www.smartthings.com/compatible-products under “Doors/Locks” and look for the “Open/Close” sensor types. There are others that aren’t on that list, but I’m not sure if you could get them in the UK.
V Multi sensors are generally more costly than single-purpose sensors. So I’m sure you can find something less expensive. Still, £30 is a fairly typical price if not on sale.
The multisensor can detect motion, acceleration, and a couple of other things.
Most people start with what are called “reed sensors” or open/close sensors" or “door/window” sensors. These are all the same thing. It’s a two-piece device that is a sensor plus a magnet. And it just tells you if the magnet is close to the sensor or not. So with two pieces, one piece goes on the door frame, One piece goes on the door. When the door is open, the magnet is moved away from the door so you get the open notification. When the door is closed, the magnet is close to the sensor so you get the closed notification.
The first place to check would be the official “works with smart things” compatibility list for the UK.
After that, pretty much any certified zwave open/close sensor should work if it’s on the European frequency. Aeon Labs (also called Aeotec) open/close sensors should definitely work with SmartThings, and many of the Fibaro simple sensors will (but not the smoke sensor yet)
Zigbee can be trickier. There are a lot of different versions of it and they don’t all work together. It needs to use the “zigbee home automation 1.2 profile” but even then there can be variations from one company to another.
I don’t know most of the European suppliers. Vesternet is very reputable, but not inexpensive. And of course you can check Amazon.