Most Volvos had very long production runs:

PV 444. Though the first prototype was shown in 1944, it was not until 1947 that limited production actually began, with full availability by 1950. The sedan was made (as a 544) until the end of 1965, the 210 wagon until 1969.

122 (Amazon) First shown in 1956, made until the end of 1970.

240. 1975-1993.

7/9 series. 1982-1999.

P1800. Shown in 58 or 9, first production with British-made body by Jensen, 1961, built until the end of 71, then two more years as a wagon.

However, lots of others have them beat, as far as longevity goes. Some examples:

The original Saab. The 92 was designed during the war and came out in 1950. It became the 93 in 1956, and that model evolved a few years later into the 96, which had a 20 year run from 1960 to 1980.

The Saab 99. 1969-1984 (rebadged "90" for the last few years)

The Saab 900. 1979-93. (later models kept the name but were GM crap)

The big Austin-Healey. 1953-67.

The MGB. 1962-80.

The Jaguar XJ6. 1968-86.

Ford Model T. 1908-27.

The Citroen Traction Avant. 1934-57.

Checker Marathon. 1958-82.

Porsche 911. The real air-cooled one. 1963-89.

The Citroen DS. 1956-74.

The Morris Minor. 1948-70.

The original Mini. 1959-2003, which seems to be the winner so far.

The Austin FX4 (London Taxicab) is up there too, but I don't know the exact years.

All of these were made by the original company, sometimes in the same factory throughout the model run. Though many of them underwent significant mechanical changes and upgrades over their production lifespans, they all remained the same vehicle, unlike, for example, the Toyota Corolla, a name which has been applied to at least a dozen unrelated models.

When you go international, things get a little more complicated. You have already mentioned three of the major ones. Many Fiats had their entire assembly lines exported when production ended in Italy, and were made for several more years in another country. The best known of these:

Lada. A 124 made in Russia. The Russians built an entire city to manufacture this car. It ran from the early 70s until shortly after the wall came down, when it was replaced by a newer FWD model.

Premier Padmini. a 1964-type 1100 (103) made in India. Started in the late 60s, ran until at least the mid-80s. Still in common use there as a taxi.

Zastava (a.k.a. Yugo) built several models of obsolete Fiats before Yugoslavia fell apart in the early 90s.

Other Fiat models continued long past their time in Egypt, Turkey and throughout South America. Several other countries similarly exported the tooling and unrelated companies built the cars. This was the case for:

The Hindustan Oxford. (the one you mentioned) Originally built by Morris, in the 50s, production started in India at some time in the 60s, and (I think) ended quite recently. They might actually STILL be making them.

Paykan. The Hillman Avenger by another name. It is Iran's national car. Not sure of production dates, but at least mid-70s until 90s.

Plenty of others as well.

Finally, cars that were built in other countries by subsidiaries of the main company:

Renault 4. First built in 1961. Production continued in Portugal well into the 90s.

Citroen 2CV. Designed and built as a prototype in 1939, but not actually built until ten years later. French production ran until the late 80s, they continued for a few more years in Portugal.

Finally, the hands-down winner----the VW Beetle. Definitive prototype shown in 1938. A few military examples during the war. Civilian production began in 1945. Last German-made sedans in 1977. However, the Beetle was assembled or manufactured in several other countries--Yugoslavia, Nigeria, South Africa and Thailand among them. The most important were Brazil, who built Beetles until 1987, and Mexico, where they ran until 2002. This equals an uninterrupted production run of 57 years, for a car that, by the end, was completely different from the original, but still very much the same. Almost none of the parts were interchangeable between 1945 and 2002, but the basic concept, shape, and dimensions remained the same throughout. The Type II (Transporter or Bus) has almost as long a history---first built in 1950, it ran until very recently in Mexico and Brazil.

I am sure there are others I have neglected to mention, but none of them beat the Beetle. I intentionally left out the Morgan and the Avanti, as they are both hand made in small quantities, and don't really qualify as "production"