Thousands of bleary-eyed, late night television viewers have lost an old friend - 890 National Press Building.

That address has appeared on television screens throughout the Washington area for almost five years, as the place to send for anything from the Miracle Slicer to a copy of Guy Lombardo's Greatest Hits.

But in the past few weeks the Telephone Answering Service Co. (TASCO)) has moved its marketing operation out of the Press building to new offices at 2208 Wisconsin Ave.

Since TASCO gave its potential customers the choice of writing or calling for products, the National Press Building Corp., which owns the building, was happy to see the firm go.

"Sure we're glad to see them go," said one building official. "We would coustantly get phone calls from people who didn't get the number off the television screen, so they look up National Press Building in the telephone book and called us."

"That caused problems," said TASCO sales manager Ann Brothers. "We offered to answer their phones for them, but they didn't want that."

But what triggered the move was TASCO's consolidation effort, designed to bring most of its activity - previously spreadout over Washington, Virginia and Maryland - under one roof in the District.

"We were faced with growing telephone tariffs in Virginia and Maryland," TASCO's Executive Director for Washington , Billie Kolb, said. "So we made the decision that in some cases it would be adventageous to centralize in Washington and reach out with our phone operation."

The bulk of TASCO's business is not mail order sales, but telephone answering services. A small office will be maintained in Room 894 of the Press buildig to handle the phones for several clients - including many residing in that building. In addition, the firm has a mobile telephone service and telephone "beeper" service.

But the mail order business was a busy one. Tasco accept the telephone orders and mail for products that were promoted by agencies in New York, Chicago and other cities. Those firms paid for the advertising time for the products.

"We just forwarded the orders and mail directly to the firm that hired us," said Kolb.

According to Brothers, one of the biggest sellers was a gospel music album by Elvis Presley, which was sold shortly after his death last summer.

"We were doing 600 a day for a long time," she said, adding that sales of the album "were strong until the end of last year."

Other favorite products were the Tummy Trimmer, the Slip cycle and other exercise machines, as well as record albums such as County Music Classics and James Cleveland's "Oh, Happy Day."

But business wasn't restricted to just records and kitchen devices. Apartment Life and Popular Sciences magazines, the Book of Knowledge, and sports card companies were TASCO clients.

As its peak, TASCO rented eight rooms in the Press Building and had seven people on the switchboards at once, with a crew of backup operators on call.

In the month of January alone, TASCO's telephone and marketing operation took in $10,000.

According to Brothers, business is always brisk at the beginning of every quarter - the first weeks of January, April, July and October - "because that's when companies budget their advertising."