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As a child, I saw a movie whose premise is that an abandoned Earth-made spaceship returns to Earth, leaving scientists perplexed. Meanwhile, an astronaut wanders the streets, slowly turning into an alien creature.

The film concludes with a giant creature being destroyed by military firepower.

It was filmed in black and white. I'm guessing it was shot in the fifties. I haven't seen it for 40 years; it was on somewhere in the late 1970s or 1980s.

I think Daniel Roseman has it almost right, and what you saw was actually The Quatermass Xperiment, the 1955 theatrical film based on the 1953 television miniseies. The story follows the same outline as the six-episode serial, described in this was by Wikipedia:

Three astronauts are launched into space aboard a rocket designed by Professor Quatermass, but the spacecraft returns to earth with only one occupant, Victor Carroon.... Something has infected him during the spaceflight, and he begins mutating into an alien organism which, if it spawns, will engulf the Earth and destroy humanity. When the Carroon-creature escapes from custody, Quatermass and Scotland Yard's Inspector Lomax..., have just hours to track it down and prevent a catastrophe.

The film, like the television serial, was a success, and it launched Hammer Films as a major player in the British horror film business.

There are two major reasons that any version of Quatermass shown on television in the 1970s or 1980s would have to be the film version. Firstly, the Hammer film version is feature length and thus easy to slot into a television special slot. The television version is longer, approximately three hours. Moreover, unlike the television version, the Hammer film still exists in complete form. As is the case for many BBC television productions from before 1980, most of The Quatermass Experiment is lost. (This phenomenon is famous in connection with Doctor Who, but it actually affects hundreds of BBC-produced programs.)

This sounds like the 1953 BBC serial The Quatermass Experiment:

When the spaceship that carried the first successful crew returns to Earth, two of the three astronauts are missing, and the third – Victor Carroon – is behaving strangely. It becomes apparent that an alien presence entered the ship during its flight, and Quatermass and his associates must prevent the alien from destroying the world.

Maybe Monster a Go-Go? It was made in 1965, and is awful. An astronaut returns to Earth in a space capsule, but has apparently been turned into a radioactive monster. At the end, it turns out that the astronaut is elsewhere and the monster has disappeared.

The movie can be seen here. It was also used in a Mystery Science Theater episode.