Universal Health Insurance Act of 1985 - Adds a new title XXI to the Social Security Act entitled "Basic Health Insurance."

Provides, under title XXI, for: (1) the establishment of one or more service areas within each State to deliver health care services; (2) the establishment of benefit standards; and (3) the selection of carriers through competitive bidding. Directs the Secretary of Health and Human Services in establishing the benefit standards to include the types of coverage normally provided by health insurance plans, including maternity and postnatal care and catastrophic protection.

Provides that every U.S. national and lawfully admitted alien shall be eligible to enroll with a participating carrier.

Provides that the annual premium for such insurance shall be equal to six percent of the sum of: (1) the amount of an individual's verified income; and (2) the amount of the individual's net assets.

Provides that coverage under a title XXI plan shall: (1) be secondary in payment to any other insurance or benefit plan; and (2) not require any evidence of medical insurability from any individual. Provides a premium discount to enrollees who make little or no use of such insurance.

Authorizes appropriations to carry out new title XXI in an amount equal to: (1) 100 percent of the cigarette excise tax; and (2) such additional amounts as may be required. Requires such funds to be used for making payments to to health insurance carriers for health insurance coverage contracted for by the Secretary under title XXI. Amends the Internal Revenue Code to impose an additional tax on cigarettes.