What you have found is "perfectly usual" and almost normal.
Inside an LED lamp will be a small switching circuit (basic SMPS) that converts the incoming 230v 50Hz to a very low voltage, DC, current source to drive the individual LEDs which may be in series, parallel or a combination. The circuit can run at anywhere from 10Khz right up to 500kHz or potentially 1MHz.
The leakage of noise from the lamp cannot be easily avoided - it will be both radiated and conducted. Because of the production process and desire to keep costs down very little consideration is given to shielding and repeatability - so two lamps produced in sequence may run at a different frequencies and may have varying amounts of shielding.
Some points to consider - where does the phone line run in relation to the lighting circuits? Not just the problem one but all of them? And remember the drops to switches. To close and you will have an issue. If they cross they should do so at 90 degrees to minimise noise pick up, if they run parallel for any distance another opportunity for noise.
So, look at where the phone line runs and consider putting the modem as close as possible to where it enters the house.
Secondly, fitting ferrite cores/beads to the individual lamp feeds may help reduce the conducted noise levels - you may
will almost certainly need an electrician to do it and he will need to ensure they do not get hot
M H C
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