In 1901, a notary public could spend $10 and get a license good for five years in the District of Columbia.

It costs the same today.

On Tuesday, the City Council is expected to approve a boost in the 82-year-old fee to $30--just one small part of an omnibus bill that will raise about $40 million from a broad range of fees and taxes over the next 18 months and more than triple water and sewer rates within five years.

The action by the council, which gave preliminary approval to the package two weeks ago, is a culmination of several tax skirmishes between council members and Mayor Marion Barry. It would give the mayor the expanded rights to set many of the fees in the future without council approval.

The increases also are the latest result of Barry's efforts to avoid general tax increases by charging the city's costs of services to users--an increasingly popular taxing device used in Maryland and Virginia and other revenue-hungry jurisdictions.

Over the past three years, Barry's special User Charge Review Committee of city officials, headed by Cynthia Lehmann, has raised the costs of about 75 percent of the more than 1,000 separate fees imposed by the District.

Under the new tax bill, some fees will double. For example, the current $30 renewal fee for a plumber's license will rise to $60 while the renewal fee for a funeral director will rise to $50. Those fees were last changed in 1976.

"It is my intent that in the future all user charges will be reviewed annually," Barry wrote in a memo announcing the committee.

By far, some of the biggest increases are in the water and sewer rates that the city will charge beginning Oct. 1.

The average residential cost of water and sewer service would rise from about the current $142 a year to $393 by fiscal year 1988. The average commercial charge would go up from $212 to $805 annually.

The steep increases in water and sewer costs to consumers--an average of 35 percent in fiscal 1984--has met with little opposition despite years of complaints about the city's water-billing system.

After several embarrassing reports about erroneous water bills as high as $14,000 at the outset of Barry's reelection campaign last year, Barry dispatched City Administrator Elijah B. Rogers to speed up some improvements and the consumer complaints dropped sharply.

The January report said that "99 percent of all telephone calls are answered now, compared to an estimated 70 percent previously." The report also said customer letters are answered within 30 days and the percentage of accounts billed on time has risen from about 50 percent to 70 percent while the remainder are billed within 30 days after the department's billing deadline.

But city officials said the city is still faced with a potential deficit of about $70 million in the water and sewer department within five years without the rate increases and prepared a massive report to back up those claims last January.

"We have not asked for annual increases like most other utilities," said William Johnson, director of the Department of Environmental Services.

Officials, who have spent several years trying to reorganize the chaotic water-billing system, said they were reluctant to seek rate increases until public confidence rose in the department.

Some of the officials recalled that in 1977, the city even temporarily halted efforts to collect water bills until it could make at least some minor improvements in water billing. In 1979 and 1980, a $400,000 contract to improve the billing system had ballooned to $1.1 million and as many as 78 percent of the accounts were not billed for more than a year.

Even after the five-year increases, city officials told the City Council that the amounts would provide only a "bare bones budget and fall far short of financial needs to properly maintain departmental water and sewer facilities" and said the increases did not account for expected expenses for repairs to the city's aging water and sewer equipment and facilities.

At the end of the five-year period, Johnson said the District, which currently charges the least for water-sewer services in the metropolitan area, should have rates roughly equal to the other jurisdictions, assuming they increase their rates slightly.

Prince William County currently charges the highest average annual rate for a family of four--$442, according to the city report. Johnson said last week the county's advanced treatment facilities are largely responsible for the cost.

The District currently charges $121.60, while Montgomery and Prince George's charge $193.60; Fairfax, $181.80, and Loudoun County, $227.88.

In addition to increases in consumer costs, Johnson said his department is negotiating with the federal Environmental Protection Agency to maintain current levels of sewage at the city's $500 million Blue Plains treatment plant, one of the most modern facilities in the East.

Johnson said last week that new regulations requiring the city to reduce the amount of nitrogen and phosphorous in treated water pumped into the Potomac River could cost the city an additional $7 million a year in sludge-disposal expenses.

"On some days, the water we pump into the river is cleaner than what's in there," Johnson said. He said he expects the issue to be resolved late this year.

Other major components in the tax package include:

* A 0.7 percent increase in the city's gross receipts utility tax to 6.7 percent, a compromise plan that replaced Barry's proposal to do away with the current 6 percent sales tax on utilities and sharply increase the gross receipts tax. The measure would cost utility companies a total of about $8.7 million in fiscal 1984 and is expected to be passed along to consumers.

* The city's four-tier system of fees for motor vehicle registration would be reduced to two. Vehicles under 3,499 pounds would be subject to a one-time 6 percent excise tax and a $45 registration fee. Heavier vehicles would be taxed at 7 percent and have a $78 registration fee. The fees would boost revenue collections about $3.4 million a year.

* A $10 charge for approximately 3,000 press passes issued to news media. The passes now are free.

* Authority of the mayor to set a broad range of fees for public health services and to designate which ones will be provided at city taxpayer cost.

* A new tax category to assess construction work in progress that would raise about $1 million.

* An increase in the minimum corporation and unincorporated business-franchise tax and professional licenses to raise an additional $900,000.