Taiwanese authorities are beginning to crack down on the flourishing illegal trade between Taiwan and the Chinese mainland, most of which is channelled through Hong Kong.

An increase in the illegal traffic led to investigations in May by one of the most powerful arms of Taiwan's military intelligence network, the Taiwan Garrison Command, according to sources in Taipei.

Local newspapers in Hong Kong have reported the detention of three businessmen by the command, and the sentencing of one Taiwanese by a military court to eight years in prison for bartering directly with mainland Chinese.

A Hong Kong woman who acted as a middleman for Taiwanese traders has been denied an entry visa to Taiwan, according to Hong Kong press reports.

These moves mark the first extensive investigation into the trade, which has grown in only three years to reach last year's official total of $560 million. Diplomats in Hong Kong and Taipei say official statistics probably do not reflect the whole picture, and that last year's total may be set more accurately at $600 million to $700 million.

Hong Kong government statistics, which do not include Taiwan's indirect China trade via Tokyo or Singapore, register $540 million worth of goods sold via Hong Kong between China and Taiwan in the first four months of this year alone, an increase of 46 percent over the same period in 1984. The total for this year for all China-Taiwan trade is expected to reach $1 billion.

The Taiwanese government is afraid that Taiwanese businesses will become overly dependent on mainland orders and increase the economy's vulnerability to overtures by the communists.

Although Taiwan's 10.6 percent economic growth rate put it at the very top of Asian nations last year, its export-led economy has suffered this spring from a drop in demand from its primary market, the United States. Economists in Taipei report that demand by mainland Chinese for Taiwanese goods is keeping some Taiwanese manufacturers' order books full.

Taiwanese authorities also are concerned about an increase in direct trade between Taiwan and the mainland, a trade the communist authorities are openly encouraging in defiance of Taipei's stringent ban.

Until recently, such trade consisted mostly of casual exchanges of fish and traditional Chinese herbs and liquors between fishing vessels from both coasts plying the Taiwan Straits.

However, the trade now includes mainland raw materials and Taiwanese consumer goods. One Taiwan newspaper linked reports that Communist Chinese authorities were purchasing Taiwanese currency notes in Hong Kong with suspicions that the Taiwanese-denominated cash would be used to pay Taiwanese businessmen and protect them from detection.

According to Communist Chinese trading agents in Hong Kong, the mainland province closest to Taiwan, Fujian, openly designated nine of the province's port cities as receiving points for Taiwanese goods this spring. Fujian trading corporations with offices in Hong Kong say they have received official directives from central authorities to expand direct trade with Taiwan whenever possible.