A baby who broke with royal tradition was born today in St. Mary's Hospital, Paddington, - a National Health Service hospital in a rather rundown area of London. Capt. Mark Phillips was there as Princess Anne gave birth to her first child - a boy weighing 7-pounds, 9 ounces. Both mother and baby are doing well after a "normal, natural birth."

The baby is fifth in line to the British throne but he came into the world plain Master Phillips, the first child to be born to a princess without a title here for at least 500 years. Princess is a "style," according to Buckingham Palace, and designation cannot be passed on.

Princess Anne and her husband are understood to have told the queen that they felt a title would be a hindrance in the child's future career.

He will probably have to earn a living. It is almost inconceivable that he will ever be king. As Prince Charles, Prince Andrew and Prince Edward marry, Master Phillips will almost inevitably slide gradually down the line of succession.

Queen Elizabeth II had the pleasure, in the year of her Jubilee, of announcing to the public that she was a grandmother. She arrived 10 minutes late for an Investiture at Buckingham Palace this morning and told those waiting for honors and titles to be conferred: 'I apologize for being late but I have just had a message from the hospital. My daughter has just given birth to a son." A cheer went up and there was enthusiastic applause.

That the queen should not have conferred a title on Mr. and Mr. Phillips - as she did in the case of her sister, Princess Margaret - for their child to inherit has caused considerable comment here.

The prospect of a titleless royal child had provoked the conservative Sunday Telegraph to editorialize: "The decision not to give a title to Princess Anne's child, though the baby is fifth in line to the throne, is a remarkable one. It shows, among other things, how strongly the tide has turned against all hereditary titles. Yet is it right that this tide should so silently engulf - or be embraced by - the Crown itself?"

Patrick Montague-Smith, editor of Debrett, the Who's Who of the British aristocracy, noted how things had changed. Not so long ago a princess would have married a prince or a Peer of the Realm and a title for the offspring would have been automatic, he pointed out. "I suppose its the trend now," he said, perhaps a little sadly.

For the most part, however, the popular verdict was that master was a good enough title for a child of 1977.

Princess Anne also broke with tradition by having her baby in the hospital. Almost without exception, royal babies have been born at home.

It was only in 1944 that the home secretary was relieved of the duty of being in the anteroom of a royal birth to insure that it was entirely what it professed to be. Legend has it that this custom started in 1683 when it was rumored that a spurious Prince of Wales was smuggled into St. James's Palace in a warming pan as son and heir to James II.

The princess went to the hospital because that was the preference of the queen's gynecologist, Mr. George Pinker. (In Britain, specialists are never called "Dr.")

She went to St. mary's, the hospital where Sir Alexander Fleming did his research on penicillin, because Mr. Pinker is a consultant there. Before the birth Pinker said Princess Anne would be treated "the same as any other patient." Afterward, a palace statement read: "Princess Anne's labor started naturally, both labor and delivery were perfectly normal and there were no complications."

When the queen arrived at St. Mary's to see her grandson for the first time, she smiled and waved to a crowd of about 200 standing in a bitter wind.

Messages of congratulation began flooding in soon after the birth, including "warmest congratulations" from Prime Minister James Callaghan.

One Labor MP, the fervent anti-royalist Willie Hamilton, was unmoved, however, "How charming - another one on the payroll," was his comment.

A comparison between Princess Anne's birth and her son's gives a glimpse of how greatly Britain has changed in the intervening 27 years. Anne was born in the splendors of Clarence House, the queen mother's home, in a room overlooking the Mall and St. James's Park.

Anne's $100-a-day private hospital room overlooks a grubby yard, the offices of a car rental firm and the murky waters of the Grand Union Canal.

The room is described as spartan. Its furniture includes a wooden-framed bed, a couple of chairs, a picture of a horse and a black and white television.

The break with tradition is not complete. In a couple of days the princess is expected to move into Buckingham Palace and the baby will follow the royal infants of recent years into the palace nursery. There he will be looked after by Miss Mabel Anderson, who was nanny to all the queen's four children. In the palace nursery is the crib made originally for the queen 50 years ago and occupied by every royal baby since.

The baby will be pushed around the beautiful gardens of Buckingham Palace in the black leather carriage used by Princes Andrew and Edward. The baby will also inherit hoards of battered family cuddly toys, and if one of London's more formiable columnists is to be believed, the baby will also have the benefit of the diapers used on Prince Edward 14 years ago.

One time-honored custom had to give way to the pressure of current events. A 41-gun saluate fired at Hyde Park to mark the birth of a royal child had to be canceled. The King's Troop, Royal Horse Artillery, was on standby duty because of the strike by Britain's firemen. Instead, Master Phillips had to make do with a single 41-gun salute from the Tower of London.

During the later stages of her pregnancy, Princess Anne was supervising alterations to her new home, Gatcombe Park, which the queen bought for her 18 months ago for about $543,000. Only the final touches to the stables of the 1,200-acre estate remain to be done and the Phillips family is expected to move in before Christmas. The day and night nurseries at the 18th Century Gloucestershire House are both ready.

There is speculation that Cpt. Phillips will soon give up his desk job at the Ministry of Defense and breed horses, the couple's spare-time interest, if not passion.