British Parliament entering television age - inch by anxious inch

The television cameras are about to enter the mother of parliaments - invited in by the not-so-fusty House of Lords. The peers, assembled on their red leather benches and beneath crystal chandeliers, have decided that the House of Commons for too long has hesitated to allow TV coverage of its proceedings.

So the upper house will take the lead with a six-month experimental period of coverage, starting next month.

Lord Whitelaw, leader of the Lords and deputy prime minister, urged their lordships to cooperate wholeheartedly with the experiment. He let it be known that he hopes the politically more powerful Commons will follow suit swiftly.

The British Parliament has been under mounting pressure to allow TV reporting of its proceedings for well over a decade. Radio coverage is an established fact , but the decision to allow microphones into both the lower and the upper chambers was taken only after lengthy heart-searching.

The Lords, by comparison, appear to have decided to embrace television in a sudden fit of enthusiasm. Prime Minister Margaret Thatcher is said to be none-too-pleased with their decision.

Her advisers point out that the experiment is likely to be costly. Some also note that TV coverage is likely to attract public attention to the activities of the House of Lords, where government defeats are much more common than in the lower chamber. And because its proceedings will be screened, viewers may conclude that the House of Lords is more important than it actually is.

An even deeper concern of the Prime Minister is that a successful experiment in the Lords may make it impossible to resist TV reporting of the House of Commons any longer. A number of her ministers are not exactly telegenic, and not all of those that are can be termed Mrs. Thatcher's favorites. Television coverage of Commons debates could turn some of the prime minister's critics into stars and make some of her most loyal lieutenants seem ineffectual and boring.

Hardened observers of Parliament believe the Prime Minister should not worry too much about the House of Lords upstaging the Commons. Many peers are apt to slumber through debates, and some are less-than-rivetting performers.

''Sleeping does create a problem,'' admitted Lord Whitelaw in debate. ''One has an option: to sleep and be televised sleeping, or not to sleep. On the whole , if I happened to fall asleep and was televised sleeping, I would not greatly mind, provided it did not happen too often.''

More seriously, advocates of televising Parliament point out that the presence of the cameras may encourage members to behave themselves better than they do now. Most debates in the House of Commons are marred by braying and bragging, and occasionally scenes of bedlam erupt on the floor.

This is one of the arguments used by the leading TV interviewer, Sir Robin Day, who has long favored television coverage of Parliament: ''The public have a right to see what happens in Parliament, and the best way to show them is to allow the cameras in. It is one of those things that must happen eventually, so why not now?''