In the first recording a voice, which is believed to be generated by a software programme and has an American accent, can be heard speaking to an official at the anti-terror hotline.
The caller claims to be called Robert West and tells the official: "I got some terrorism for you here."
After explaining that the call was from the group known as Teampoison, he tells the official: "Our philosophy is pretty simple, it's knowledge is power."
The call lasts several minutes before an official tells the caller that they are terminating the conversation and passing the details to the FBI.
In the recording between officials, one person can be heard telling another that the hotline received more than 700 phone calls from the group.
He is heard to say: "We have been subjected to a barrage of calls from a group called Teampoison. We have had about 700 calls over the last couple of nights. One of the conversations I had last night was leaked on Youtube.
"Everyone else calling was effectively shut out and could not through at all."
A statement from the Metropolitan Police Service said: "We are aware of an issue whereby telephone conversations relating to the anti-terror hotline were recorded. Officers are currently looking into the matter and appropriate action will be taken."
It is the second time in a matter of months that hackers have gained access to private telephone conversations involving Scotland Yard personnel.
In February hackers from the group known as Anonymous released a recording of a conference call between the FBI and UK police in which they were discussing efforts to catch hackers.
Last week the Home Office website was also targeted by hackers from Anonymous closing it down for at least an hour.