When you turn 80, the NHS offers a free health check-up, including a memory test. Having reached the qualifying age earlier this year, Sheila Hancock went along for hers. "At the beginning," she recalls, "they gave me some things to look at, and then came back later to see how much I could remember. And they kept saying, 'Don't worry. You're not expected to remember all of it.' But actually, as it turned out, I could."

Hancock suggested to the impressed medics that the discipline of learning lines may actually protect actors from memory loss. "They were interested in that – and there's a possibility now that I may take part in a clinical trial."

Hancock features in one of two big openings in London's West End this week which reinforce the notion that, both on screen and on stage, performers have traditionally worked for as long as their health lasts and the opportunities still exist. She has a lead role in Clive Exton's foul-mouthed farce Barking in Essex, while James Earl Jones and Vanessa Redgrave play the reluctant lovers Benedick and Beatrice in Much Ado About Nothing. At 76 and 82, Redgrave and Jones are almost twice the age at which actors have traditionally played the squabbling couple. In his previous theatrical pairing, Jones was the junior partner, co-starring in an Australian production of Driving Miss Daisy opposite the 87-year-old Angela Lansbury.

However, such positive images of acting longevity have been countered by two leading men apparently contemplating retirement. Earlier this month, rumours emerged from Hollywood suggesting that Jack Nicholson, now 76, may have made his final film, after reportedly struggling to learn lines. Although the triple Oscar-winner has since denied these claims, the increasing difficulty of memorising a part was cited by Michael Gambon, who spoke of having suffering stress-related illness during recent theatre appearances. This perhaps explains why Gambon's most recent stage roles have been in three Samuel Beckett plays: Eh, Joe?, Krapp's Last Tape, and All That Fall. Respectively, his roles in these works have been: silent; largely tape-recorded; and with a script in his hand.

Although Hancock may have impressed the medics at her checkup, she admits that preparing for her first West End appearance as an octogenerian has taken its toll. "I certainly find that I get more tired," she says. Although she found Barking in Essex hard to commit to memory, she was relieved to discover, during rehearsals, that younger cast members – including Lee Evans, 49, and Keeley Hawes, 37 – had reported the same difficulty and so attributed it to the idiom in which the script is written, rather than encroaching senility.

Derek Jacobi in Last Tango in Halifax. Photograph: Vish/BBC

Coincidentally, the structure of Derek Jacobi's memoir, As Luck Would Have It, published last week, directly reflects the effects of passing time on an actor. The book's seven chapters are based around the "ages of man", as outlined by Jacques in As You Like It – a passage that has been driven into the heads of so many UK schoolchildren that it may well be one of the final things that elderly Britons forget. In the final section ("second childishness and mere oblivion", according to Shakespeare), Jacobi expresses the hope that there is "much more to come" after his 75th birthday. When I talked to him about the book, he stressed that he wants to "go on until I drop". After filming the new series of his BBC1 drama Last Tango in Halifax and his ITV sitcom Vicious, he hopes to return to theatre in 2015, when he will be 76, ideally in a new play.

In the earlier part of his career, Jacobi was celebrated for his powers of memory – once playing, in rapid and sometimes alternating succession, the parts of Benedick in Much Ado, Prospero in The Tempest, Peer Gynt and Cyrano de Bergerac. So, a month before his 75th birthday, does Jacobi retain this power? "It's pretty much there still," he says. "I feel desperate for Michael [Gambon] and lucky that I don't have that problem. The consolation is that he still has that great screen career."

Gambon will, in fact, return briefly to the stage when he plays, with Jacobi, a scene from Harold Pinter's No Man's Land during the National theatre's gala event in November to mark its 50th birthday, although the chosen extract gives Jacobi most of the lines. Another overlap between the actors is that Gambon reports having been hospitalised with stage-fright, a condition that Jacobi also discusses in his book: after more than 300 performances as Hamlet, he suddenly forgot the words of "To be or not to be" and stayed away from theatre for two years, suffering recurrent panic attacks.

Jacobi says that experience, in middle age, places a bigger question over his theatrical longevity than the approach of old age: "I still have the vestiges of that fear. Once you've had it, it's always there. If I ever did stop stage acting, it wouldn't be because I was worried about not having the physical or vocal capacity, but because of the stress. I do get very frightened."

Hancock also acknowledges that stage work makes demands that can't be tested in a medical: "I have started to feel – which is new for me – that, at 80 and with limited years left, I'm not sure I want to go on giving months to the discipline of theatre. I write, I do other things. So I think there is a question now over how long I'd want to go on doing theatre."

Even if their memories remain supple, older actors are statistically more at risk from illness and injury: earlier this year, 87-year-old Robert Hardy had to pull out of The Audience, Peter Morgan's play about the Queen's relationships with her PMs, after a fall; and certain horror stories circulate in the profession, such as the case of the elderly performer who lost control of his bladder on the stage of a major theatre.

James Earl Jones and Vanessa Redgrave in Much Ado About Nothing. Photograph: Tristram Kenton for the Guardian

Senior cast members must accept, says Hancock, increasingly stringent medicals after being offered a part, for the purposes of insurance. "Although," she says, "I would maintain that, in some ways, I am probably in better shape now than when I was young, and used to do all sorts of bad things, which I've stopped now."

Another drawback of ageing, it is often said, is that the range and number of parts reduces. "Personally, I've been lucky," says Hancock. "Although I know that it is a problem for some people. I think you just have to accept that the roles will progress from lover to mother to grandmother, and so on. Sometimes producers approach my agents and say, 'Would Sheila be offended if we offered her the part of an old person?' And I say, 'Look, I am fucking old! Don't be so silly!'"

Jacobi's part in Last Tango in Halifax – his biggest TV role since I, Claudius in the 1970s – arose from a deliberate effort by television producers to make shows for older viewers, a strategy that should result in more work for older performers. "I think the success of that series has shown," says Jacobi, "that there is a demand for stories that put older people at the centre. To some extent, it has started a trend."

If new parts are in short supply, then an alternative is to follow the Redgrave/Jones Much Ado About Nothing (and a 2010 Bristol Old Vic Romeo and Juliet, in which the star-crossed lovers were in their 80s) by simply ageing the characters in classic plays. Hancock says that she would love to be in a revival of Noel Coward's Private Lives, in which divorcees Elyot and Amanda split after their golden wedding anniversary, rather than after just three years together. So they would now be with much younger partners. "I think the sense that they had had a really long marriage – and had then taken a last chance of escape in old age – would bring something new to that play."

Jacobi, meanwhile, feels highly optimistic at the thought of this imminent and elderly Much Ado. "If it works for Vanessa," he says, "we'll all be doing it. Perhaps I'll finally get to give my Romeo!"

• Barking in Essex is at Wyndham's, London WC2 (0871 976 0072). Much Ado About Nothing is at the Old Vic, London SE1 (0844 871 7628). As Luck Would Have It by Derek Jacobi is published by HarperCollins.