I'm going to leave this link here:
Basically these one of the incredably common non standards compliant christmas lighting sets you can buy online from places over in the east!
Issues generally are that they are wired in very thin wire which also with poor insulation, and are often supplied with a non compliant plug that either has no fuse(like yours) or a conterfeit fuse). They also feed the LEDs in long strings straight from rectified mains, which would be alright if the insulation was upto it, but A) its very thin. B) terminations to the LEDS are via a heatshrink soldered joint, which can let dampness in and can let the cables pull out if handled roughly, and some sets have even be found with stray whiskers on the connections from new.
With LED christmas lights there are basically two ways they can be done:
1) Use a separated extra low voltage power supply with appropiate current limiting and don't worry too much about the robustness of the light string.
2) Use rectfiified mains, but make the light string very reobust with proper water sealed connections, insulated and sheathed cables, and of course fuse them appropriatly.
Most Domestic sets will do 1), while generally a lot of the sets designed for installation in city centres, parks etc do 2) but also generally they are kept at a height that can't be reached by the public as well
If you must keep using your lights, then fit a plug with a 3A (or even better 1A) fuse, but thats rather like telling you that you should wear your seatbelt when driving a car with no brakes - it is clearly an improvement on not doing so, but it is still far from safe
