Your drop arm has fatigued and given up the ghost, although if it's the front axle, this may have been helped along by kerbing...
The easiest way to tell the weight capacity of the axle you need is to look at the chassis plate (should be n/s/f of the trailer chassis) and see what the GVW (gross vehicle weight) of the trailer is and then divide it by the two axles.
i.e. if your GVW is 2000kg then each axle capacity is 1000kg
Additionally, as they're Alko axles there should be an axle plate riveted to the rear face of the axle (check both, in case one has fallen off). On this will be stated the axle type (i.e. part number), it's capacity and date of manufacture. With this information you will be able to get an Alko axle from any Alko dealer, meaning you're not reliant on just the trailer manufacturer. Expect to pay around £300 for a new Alko axle.
Your idea of fitting box section and units is ok, but it will mean that if you don't do both axles then one will be higher / closer to the ground than the other and therefore will take more load than the original one. Bear that in mind 'beef' it up a little more than required.
How far is the workshop? If it's close by then it's possible you may be able to drop the knackered axle out the way (only four bolts) and tow it (carefully!) on the remaining axle...