A subsidiary of Kemper Corp., a major insurance and financial services company based in Chicago, has acquired Washington's Cranston Securities Co. and will consolidate the unit's securities underwriting and other government-related operations in the District.

Cranston, a private Washington-based securities firm that has been aggressively seeking a local D.C. bank charter, was purchased by Prescott, Ball & Turben, Kemper's general service brokerage firm based in Cleveland. Cranston Securities was renamed Cranston/Prescott on Friday, when the deal was completed, according to Robert Cranston Kanuth, chairman of Cranston/Prescott.

The purchase price was not disclosed.

The sale will enable Prescott and Cranston to combine and consolidate their government-related activities, which include underwriting government bonds and acting as financial advisers and managers to governments. Kanuth said the consolidation will give Cranston/Prescott added clout in the industry and substantial operations in Washington.

Prescott has 1,300 employes Kemper earned $93.3 million on revenue of $2.5 billion in 1985. Kanuth declined to release revenues for Cranston.

Cranston/Prescott will be based in Washington, and no layoffs are anticipated, Kanuth said. Cranston Securities had about 100 employes, with about half of them working in the Washington office.

Both Cranston and Prescott have sought local D.C. bank charters. Cranston Securities has, in particular, been in the forefront of the heated, high stakes battle Washington-area bankers have fought to block new banks from coming into the District.

Kanuth said both Cranston and Prescott will continue to seek bank charters in the District. Both securities firms have received preliminary federal approval for local bank charters from the Office of the Comptroller, according to Kanuth. He said they are now awaiting approval of federal deposit insurance, necessary for opening a bank.

Eleven groups applied for D.C. charters in the fall of 1985 and spring of 1986, in an attempt to take advantage of a loophole in federal banking law that was closed in April 1986.

Under a 1901 federal law, banks were able to seek a D.C. license from the comptroller of the currency, rather than a state or federal charter, which is required of national banks and state banks in other jurisdictions. Because most federal regulations apply to state and federally chartered institutions, these new banks appear to be outside the reach of those laws, giving them power to offer services denied other banks.

In April 1986, the power to charter local banks was transferred to the D.C. government. But the application by Cranston, Prescott and the other nine groups came under the old law.