I was once taken to a cricket match in Bombay by Shashi Kapoor, the great Bollywood star, who has died aged 79. As his open-topped car sped from his house to the ground, whenever it was forced to stop at the frequent traffic lights, a crowd of admirers would gather, clapping, shouting and begging for autographs. He signed willingly, sometimes holding up the traffic, and when we reached our seats at the cricket ground, he spent almost the entire day signing again. I asked him why he was so generous with his time, particularly as he was really interested in the match. “Look, Derek,” he said. “I owe everything to these people. It’s my way of saying thank you.” He was not only the most handsome leading man in Bollywood, but also the most charming and modest.

English-speaking audiences will remember him best in Merchant Ivory films such as The Householder (1963), Shakespeare Wallah (1965) and Heat and Dust (1983), and for these he willingly accepted far less money than for the Bollywood movies that made his name. Trained in the theatre, he took his acting seriously and often laughed at the fact that he had to make three or four Bollywood epics at a time and had no idea as he went from set to set what he was supposed to be doing, and who he was supposed to be doing it with, let alone what he was pretending to sing, as the playback singers did the real business behind the scenes. “It’s all a game,” he told me, “and I am very fortunate to be asked to play it. But sometimes it’s a bit too much.”

In fact, he appeared in some of the best Bollywood films of his era, opposite the greatest stars in the business. His looks carried him through all the absurdities of the song-and-dance numbers. Although the list of his hits at the box office is endless, he made a good many bad movies too. As a producer for his own company from the late 1970s to the early 90s, he had less success than he had been used to, despite critically well-received productions such as 36 Chowringee Lane (1981), which starred his wife, Jennifer Kendal.

Shashi was a member of the famous Kapoor family, who dominated the Bollywood scene for decades, particularly through the influence of Raj Kapoor, Shashi’s elder brother. Raj made hit films such as Boot Polish (1954), nominated for the Palme d’Or at Cannes, and Shree 420, the highest grossing Indian film of 1955. If Raj was considered the Clark Gable of India, Shashi was his country’s Robert Redford.

Born in Kolkata, son of Ramsarni Devi and Prithviraj Kapoor, Shashi was already on the stage as a child in the 40s, acting for his father’s repertory company Prithvi Theatres, as his brothers Raj and Shammi had done before him. The movies soon followed, among them Aag (1948) and Awaara (1951), both directed by Raj, and considered classics now. Shashi then became assistant director for Sunil Dutt, who was making Post Box 999 (1958).

Success followed as a leading man in more than 60 Hindi films, in which he appeared with the most notable female stars of the time. One of his favourite leading ladies was Nanda, with whom he made eight films and whom he regarded as his mentor. Others he worked with included Raakhee, Sharmila Tagore, Zeenat Aman, Hema Malini and Parveen Babi. He also made a dozen films with Amitabh Bachchan and appeared with almost all the male stars of the period. He was well paid for his work, but somehow managed to lose much of his fortune, perhaps through sheer generosity and the fact that he was not a good businessman.

He became increasingly bored with commercial Hindi movies and charged into films such as Bombay Talkie (1970), Siddhartha (1972), Junoon (1978), New Delhi Times (1986) and In Custody (1994) with some relief. The 70s and early 80s were a good period for more challenging independent films and Shashi took full advantage of the freedom they gave him.

Though the cinema made him, theatre was his first love, and he did everything he could to encourage the stage in in Bombay (now Mumbai), with money and help. Shashi’s work in establishing the Prithvi theatre in the city, in memory of his father, was outstanding. Jennifer helped supervise and run the theatre for many years.

She was the daughter of Geoffrey Kendal, who had toured the Shakespeareana acting troupe around India, and upon whom Shakespeare Wallah was loosely based. Both Jennifer and her sister, Felicity, acted with Shakespeareana in the 50s. Jennifer and Shashi met in Kolkata in 1956 while each was appearing with their father’s company and they married two years later. It was thought that Shashi never fully recovered from the shock of Jennifer’s death in 1984 from cancer. He died from complications of long-standing heart and liver problems and while in hospital insisted on meeting and attempting to help other patients.

He is survived by their three children, Kunal, Karan and Sanjana.

• Shashi Kapoor (Balbir Prithviraj Kapoor), actor and producer, born 18 March 1938; died 4 December 2017