Decades ago I worked in AM radio. A listener was using a reel to reel tape recorder with an un-grounded mike (or aux) wire which picked up the AM signal and it was demodulated.
My bet, something along your chain is un-grounded and is picking up a local AM broadcast tower nearby. I have seen it on regular landline telephone lines.
Radio and television stations in the U.S, identify themselves at various times but always at the top of the hour.
The phone company oftentimes had filters for landline, but if you are not using one, then you have to investigate yourself. When this happens, can you move your hand around each item, OBI, cordless phone, etc to see if the signal increases ort decreases. The item you touch may well be the culprit.
The cure can be something as simple as a ground wire or a capacitor to shunt the signal to ground.
You might look to a local "Ham" amateur radio operator for help (not that it is their fault, but they are great at looking fo this type of thing).