CAPE CANAVERAL, Fla. (AP) _ A nuclear-powered British ballistic missile submarine preparing to dive off the Florida coast collided with a commercial fishing vessel, injuring the four people aboard the civilian boat, the Coast Guard said today.

The 425-foot Resolution and the 57-foot fishing vessel Proud Mary, out of Fort Pierce, collided about 9:30 p.m. Sunday, 13 miles southeast of Port Canaveral, said Chief Petty Officer Bob Baeten, a Coast Guard spokesman in Miami.

One of the submarine's diving fins, mounted on its hull about 100 feet from the bow, sliced into the Proud Mary's wooden hull, leaving a 15-by-6-foot gash above the waterline.

A woman crew member from the Proud Mary was hospitalized with a broken kneecap. Three other members of the crew were treated for cuts, Baeten said.

None of the 143 men aboard the submarine was believed to be injured. Damage to the submarine was unknown.

Today, the Resolution successfully launched a Polaris missile while cruising 30 miles off Cape Canaveral.

The firing provided training for the crew of the Resolution, one of four Polaris submarines in the British navy. The Resolution is commanded by Cmdr. M.J. Sime.

The accident occurred in clear weather, with unlimited visibility, Baeten said. The Resolution was being escorted by a U.S. Navy vessel, which is supposed to clear the area of traffic, he added.

''The fishing vessel was just transiting the area,'' Baeten said. ''The cause of the accident will not be known until after an investigation.''

He said a 41-foot Coast Guard boat took the Proud Mary in tow Sunday night and arrived early Monday at Port Canaveral, where temporary repairs will be made.

The submarine, commissioned in 1967, displaces 8,400 tons and carries 16 Polaris missiles and a 147-member crew.