In 1961, EMI records organised Richard's 21st birthday party at its London headquarters in Manchester Square led by his producer Norrie Paramor. Photographs of the celebrations were incorporated into Richard's next album "21 Today" in which Tony Meehan joined in despite, then, having very recently left the Shadows to be replaced by Brian Bennett.
Typically, the Shadows closed the first half of the show with a 30-minute set of their own, then backed Richard on his show-closing 45-minute stint as exemplified by the retrospective CD album release of Live at the ABC Kingston 1962. Tony Meehan and Jet Harris left the group in 1961 and 1962 respectively and later had their own chart successes for Decca. The Shadows added bass players Brian Locking (1962–63) and then John Rostill (1963–68) and took on Brian Bennett permanently on drums.
In the early years, particularly on album and EP releases, Richard also recorded ballads backed by the Norrie Paramor Orchestra with Tony Meehan (and later Brian Bennett) as a session drummer. His first such single without the Shadows was When the Girl in Your Arms Is the Girl in Your Heart in 1961, and he continued to release one or two per year, including covers of "It's All in the Game" in 1963 and "Constantly" in 1964, a revival of a popular Italian hit. In 1965, sessions under the direction of Billy Sherrill in Nashville, Tennessee were particularly successful, yielding "The Minute You're Gone", which topped the UK singles chart and "Wind Me Up (Let Me Go)" which made No. 2.
Richard's father, Rodger Webb, died in 1961, aged 56, and that had a great impact on Richard. He later said: "My father died very young. He missed the best parts of my career. When my father was sick, we became very close." Richard's mother, Dorothy, died in October 2007, aged 87, after a decade with Alzheimer's disease. In a 2006 interview, he spoke about the difficulties he and his sisters had in dealing with their mother's condition.
Richard is a lifelong bachelor. In a three-page letter written in October 1961 to "his first serious girlfriend", Australian dancer Delia Wicks, made public in April 2010 after her death from cancer, Richard wrote, "Being a pop singer I have to give up one priceless thing – the right to any lasting relationship with any special girl. I've just had to make, probably, one of the biggest decisions I'm ever going to make and I'm hoping that it won't hurt you too much." The couple had been dating for 18 months. In the letter he goes on to say, "I couldn't give up my career, besides the fact that my mother and sisters, since my father's death, rely on me completely. I have showbiz in my blood now and I would be lost without it." Richard urged her to "find someone who is free to love you as you deserve to be loved" and who "is able to marry you".