Sometimes I miss things and sometimes I lose things and I certainly do not claim to be infallible. And I never intend to be rude or insult anybody. and I do appreciate your pointing out that this was one of those times.
Sorry to have said the wrong things and delivered an incorrect impression. I just plain goofed up and will do my best to not do it again.

 

The reason why 20 twelve volt lamps in series works on 240VAC is because each lamp drops 12 volts across its filament. LED's don't quite work like that. To use 20 LED's in series would require a lot more effort than you think. For instance, each LED has its own forward voltage drop (Vf) Red colored LED's tend to have the lowest Vf while blue and white the highest. And with different manufacturers those numbers change. You can't compare one red LED to another if they are not manufactured at the same time, same place, same machine. Those variances will make a huge difference in the way the LED's perform. And since the primary difference in voltage requirements for incandescent lamps versus LED lamps means, and this is purely a guess, running 20 varied colored LED's in series means you can have a Vf of between 40V and 60V. That depends on how many of what colors you have. This means your 240VAC supply will blow out a bunch of LED's frighteningly quickly.

OK, so you think you can put a resistor in series to limit the current. Yeah, that's a possibility. But not recommended. That resistor is going to get hot. Without knowing specifics I can't guess at how many watts the resistor would need to dissipate. THEN there's the complexity of making sure all the LED's are polarity correct. Once you've overcome all that - there's yet another devil in the details. LED's don't like reverse voltage. They will tolerate a small amount of voltage but at 240VAC, they're going to go the way of the devil in hell himself.

LED's are current driven devices whereas standard lamps are voltage driven. It takes 12 volts to light a 12 volt incandescent lamp whereas an LED can be driven from a greatly varied voltage. As long as you limit the current to what the LED is rated for you can (in theory) power it from thousands of volts. Running a red LED with 2Vf at 12 volts (DC) with a current of 10mA means you're going to need a 1KΩ resistor. That will limit it to 10mA. That same LED can be run from 24VDC at 10mA using a 220Ω resistor. And again, with 48VDC and 10mA, the resistor is 4.6KΩ. While you can do the same thing with incandescent lamps the resistors required will have to be different values and higher wattages. That means you're wasting more current as heat energy.

Sadly it's not so straight forward as simply replacing an incandescent bulb with an LED bulb. The lamps you use in the home for light are designed to operate on their respective voltages with the internal electronics providing the proper current for the LED's inside the lamp. There is no electronics inside an incandescent lamp. It works on its rated voltage and that's it.

I foresee a lot of rewiring of your string of lights in order to get the effect you want. And all that rewiring might be far more unsightly than using some hot melt glue to glue on those fancy shades you want to use.

I miss Christmas of old. When I was a child. The colored lamps, their warm glow, their soft colors. LED lights attempt to achieve the same thing but they're just not the same. They lack the charm I grew up with. For my grandchildren it's a different story. What they're growing up with will be dear to them when they're in their old age. Life moves on. Change is the only thing I've observed to be a constant.

I think then
I too remember the good old Pifco lighting sets my parents had, 12x 20V in my case, with the bare conical screw-in bulbs, a lovely soft glow and the fun of playing hunt the faulty bulb though to be honest they were very reliable. And having looked at my contemporary led lighting and white tree during this christmas period have vowed to go back to a green tree and nice warm lights to recreate my childhood memories, now wheather I will be able to find genuine incandescent lighting sets from that era, or copies thereof, is going to be a fun challenge.

 

For LEDs IN SERIES, the current will be the same in every one of them. THAT is the way series circuits work. And certainly the forward voltage drop may not be the same for each of the LEDs in the series string BUT it does not matter at all, if they are all rated for the same current. For series connected LEDs it is important that the current be limited to the specified amount, or a bit less. For white illumination types of LEDs the current may be quite a bit more than 20mA. This is where it becomes very useful to know the type number of the LEDs in the string, or at least have the data sheet. Another option is to take data , both forward voltage and current, while applying power and watching the LED illuminate. Usually the graph of forward voltage versus versus current shows a greater increase in current for the same step in voltage as the specified max current is reached and exceeded.. So that is the scheme for figuring the current to run them at. ( to do this you do need a voltmeter with at least ten millivolt resolution and the ammeter with at most ten millivolt resolution. The accuracy is not as important as the resolution because you are looking for the shape of the curve, not the exact values. The normal forward voltage for white LEDs is in the range of 2.6 volts to 2.9 volts, and the current may get as high as 100 milliamps.

 

For LEDs IN SERIES, the current will be the same in every one of them. THAT is the way series circuits work

I'm not arguing this point. It's what I believe to be the truth regarding series LED's just as @MisterBill2 says. HOWEVER, for reasons I don't understand I just scrapped a number of strings of LED Christmas lights because the blue LED's were burning out while the rest of the string continued to illuminate. I DON'T KNOW WHY THAT HAPPENED. Also, in a series circuit, if one bulb fails then all would go out, just as you said. BUT, and here's another part I don't understand, when you remove a bulb the string goes out. But when one bulb (LED) goes out the rest remain lit. Just how that is - I don't know.

I, too, miss the charm of the small incandescent lamps on the tree my parents used to set up when I was a wee lad. Yes, way back then they had electric lamps. I deeply miss the warm glow of the bulb the LED versions try to emulate. They just lack that charm.

 

The explanation for why one LED failing does not darken the whole string is simple, lust like it is for the series bulbs.when the illumination part fails open, the bypass device passes the current. In a filament type bulb it is a breakdown of insulation of the bypass jumper that completes the circuit. In an LED it is a device similar to a varistor that passes the current after the voltage rises.
And the BLUE led devices failed because the blue forward voltage is higher , and also because blue LEDs cost more for good quality, so poor quality was used.