Is that a RedMax? The BCE24F looks similar to RedMax model numbers? RedMax manufacturers excellent commercial grade handheld outdoor power equipment. Though I can't find their UK site, the overall engine design and model number look similar to what RedMax would do. In the U.S. RedMax units are sold by dealerships only but I think you may be able to buy them from a few sources online which would explain your having to assemble it yourself. Buying it from a dealership they would have assembled it. In recent years RedMax was acquired by Husqvarna. Husqvarna produces a mix of handheld outdoor power equipment along with mowers, and other power products. A good line but not as good as RedMax products.
Over in the UK, and I believe Australia, they are referred to as Strimmers. In the U.S. most consumers call them Weedwackers. Some people call them Weedeaters, which personally I don't like as Weedeater is a low end cheapy, consumer model manufacturer name. Essentially the Weedeater brand to weedwackers would be like your Bissell or Dirt Devil of vacuums. Dealerships and manufacturers generally call them string trimmers. The machine you bought with the T bar handle would be a Brushcutter in the US. These have a much larger guard over blade, a protection on handle that is supposed to help keep user at a certain working distance from head. The shafts are steel straight shafts instead of flexible cable to be able to handle the blade.
Best of luck and enjoy! I love outdoor power equipment. RedMax, Echo, Shindaiwa, Kawasaki, Maruyama would all be lines that I heavily recommend anyone looking for great weedwackers, leaf blowers, chain saws, or other handheld products. I'm not a fan of Stihl products-- too loud, too much vibration, ugly, expensive parts, reliability not as good as some others. Machines have a terrible tone compared to lots of other companys.
For mowers: Toro, Gravely, Ariens, Scag, Bob-Cat, Snapper, Exmark are some excellent lines. Honda is also well recommended for walk behind mowers. I'm not a fan of the Hondas though, I think they're ugly looking and for the price I'd look elsewhere.
http://www.redmax.com/
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The other (cheaper) ones on the market with the 'curved tube' construction tend to fail rapidly, vibrating enough to bring on 'White Finger' syndrome... 
