Michael Fagan, the man who breached Buckingham Palace security last Friday morning and went to the bedroom of Queen Elizabeth II, spent "just over 10 minutes" talking with her about the royal family, Fagan's lawyer said today.

Attorney Maurice Nadeem said in an interview with Independent Television News after visiting his client at London's Brixton Prison that Fagan went to the palace "twice--no more" because "he wished to see her majesty the queen."

Nadeem said Fagan's intrusion ended when a maid entered the room and led him away.

The lawyer's account provided the latest in a series of often conflicting details on the extraordinary incident, which has outraged politicians, the press and the public here because of the serious lapse in palace security. Prime Minister Margaret Thatcher, who drove to the palace last night to apologize to the queen, called in Parliament today for "a very thorough review" of security arrangements for the royal family and said she expects to have a special police report by next week.

Earlier today, Fagan's mother told British reporters that her son said he visited the palace repeatedly in recent months, telling his family he was going to see his "girlfriend, Elizabeth Regina"--another way of saying the queen.

"He said she had four children, like him but was a bit older than he was . . . ."--actually almost twice Fagan's age. His father described Fagan as a "royal fanatic."

However many visits Fagan may have made to the palace, it seems that only once did he actually accost the queen. After pulling himself up a drainpipe to a first-floor window sill, he arrived at her bedside about 6:30 a.m. Friday, a piece of jagged glass from an ashtray in his hand, blood dripping from a cut, and assured the monarch that he meant her no harm.

These details, which appeared in British newspapers today, were based mainly on police information, which has not been denied, and interviews with Fagan's relatives.

In the aftermath of the Daily Express story yesterday revealing the episode, other British tabloids went all-out to advance the saga today. Britain's more serious newspapers confined themselves largely to editorials deploring the serious lapse in palace security.

Two reports, one from the final edition of the Standard newspaper this evening and the second from the British Broadcasting Corp., offered differing versions of the security failures involved in Fagan's encounter with the queen.

The Standard reported that the monarch used her bedside phone to summon help after Fagan had awakened her early Friday morning, but the palace police officer did not recognize the urgency of her call, which she tried to make "sound important but not hysterical to avoid alarming the man."

The paper said a maid entered the queen's bedroom about 10 minutes after Fagan had intruded and "police arrived another eight minutes after that--when the chambermaid had already led the man away" to the custody of a footman.

The BBC reported that the monarch tried to push a "panic button" in her room but that it failed to go off.

Another account, in the London Daily Telegraph, said police at the palace ignored an alarm set off by Fagan as he made his way to the queen's bedroom because they thought it was faulty.

The Daily Express in its Wednesday edition, which was available tonight, said the queen was reported to be extremely disturbed at what she regarded as the offhand response of authorities to her alarm.

The portrait of Fagan and his exploits that emerged from today's accounts remained somewhat fuzzy.

He is either 30 or 31, unemployed, a father of four; his wife also had two children from a previous marriage. Fagan's father was quoted as saying, "He would not hurt a fly." But it was reported that on July 5 he was accused by police of assaulting his l5-year-old stepson and released on bail.

The man's mother said, according to the Daily Express: "He is not a revolutionary in any way. He has no political affiliations."

In its Wednesday edition, the Express printed the text of a letter of apology written by Fagan's mother, Ivy Fagan, to the queen in which she said she was "shocked and ashamed" at her son's conduct and said she was grateful for the monarch's "forbearance and understanding" of a mother's grief over what a son does.

Police arrested Fagan on June 7. He was charged with trespassing and stealing a half bottle of wine and then released. He appeared again in court Saturday after police found him in the queen's bedroom. He has not been charged in that episode.

How Fagan gained entrance to the palace is not clear. He evaded sensory devices and cameras apparently by scaling the 10-foot walls covered with barbed wire and spikes. This would explain blood on his hands and, according to some accounts, on his feet as well.

After pulling himself up the drainpipe, he pulled aside a screen and entered the room. A policeman on duty at the end of the corridor had left 30 minutes earlier, when members of the queen's personal staff arrived for work.

The Scotland Yard official in charge of the investigation into the incident, Assistant Commissioner John Dellow, spent much of today at the palace interviewing officers and looking over security devices.