Norman Stanley Fletcher, who was banged up in the 1970s BBC prison sitcom Porridge, would only still be behind bars now if he had been a serial killer rather than a petty criminal who crashed a stolen booze delivery truck while driving it away.

Porridge, though, is back on the BBC’s TV schedules this week, alongside additional sentences for the characters of other classic British sitcoms. Mrs Slocombe, the shop assistant with candyfloss hair and a tendency to have anecdotes about her cat misunderstood, returns with her colleagues at Grace Bros department store in Are You Being Served? Viewers will also receive an update on Hyacinth Bucket (pronounced Bouquet), social-climbing heroine of Keeping Up Appearances – even though she might consider it a bit common to be part of a theme season.

These new gags for old lags of television comedy are part of what might be called a jestival, marking the 60th anniversary of the first British TV sitcom, Hancock’s Half Hour, which was screened in the summer of 1956. Starting on Sunday, BBC1 will screen new episodes of Are You Being Served? and Porridge, followed by Young Hyacinth, a prequel to Keeping Up Appearances, under the banner Landmark Sitcoms.

This series of one-off specials – which, in an era of cultural nostalgia, may possibly result in new series being commissioned – will certainly help the BBC with any monitoring of birth-date diversity. Hyacinth’s creator, Roy Clarke, 86, has written the script about her, while the original writers of Porridge, 80-year-old Ian La Frenais and 78-year-old Dick Clement, have also scripted its continuation. Only the shop comedy has brought in new blood, with Derren Litten, creator of the ITV holiday comedy Benidorm, standing in for the late Jeremy Lloyd and David Croft.

Each show has been revived in a different way. Clement and La Frenais have set their episode in the present-day. Nigel Norman Fletcher, grandson of the inmate played by Ronnie Barker on BBC1 from 1974-77, is serving a five-year stretch for cybercrime at Wakely, a C-list prison, rather than the higher-security Slade of the original series. The new Are You Being Served? takes place in 1988, three years after the comedy ended its 13-year run on BBC1. Located in the 1950s, before its protagonist gained by marriage her shaming surname, Young Hyacinth is even more of a period piece.

The challenge in reviving a situation comedy is how much of the sit can be changed without losing the com. Are You Being Served? is most obviously a cover version. Jason Watkins, as Mr Humphries, and Sherrie Hewson’s Mrs Slocombe offer karaoke acting, more or less copying the intonations, body language and costumes of John Inman and Mollie Sugden. And, though supposedly translated to the final Thatcher administration, the shop occupies, as it always did, the England of the 1960s, when the Carry On movies were at their height. Although Litten is only 45, his Grace Bros finds display space for many jokes much older than he is. This is a world where staff, overhearing their boss giving instructions for dealing with a length of electric flex (“It’s not long enough to go in!”) believe that he is having sex with his secretary.

Pre-transmission speculation that Mrs Slocombe’s pet obsession might be trimmed and manicured by modern BBC guidelines proves misplaced. The maven of ladies’ fashions makes numerous references to her “pussy”, although the new scriptwriter doesn’t always seem to appreciate that the best double entendres work both ways, as in Lloyd’s and Croft’s frequent variations in the area of: “The hairs on my pussy stood up on end.”

There was also a pleasure, in the show’s first incarnation, in suspecting that the BBC censors might not have been feline enough in their suspicion. In a line that Litten gives Hewson – “My pussy had a sneezing fit” – the audience, the other characters and the BBC editorial compliance department are so in on the gag that it’s effectively a single entendre.

The introduction of a new character, trouser department novice Mr Conway (Kayode Ewumi), is in line with the main innovation of the Landmark Sitcoms project: more diverse casting. Nigel Norman Fletcher is sent down by a black judge, although, to be fair to the original 1974-77 series, it was ahead of its time in the non-white character of Tony Osoba’s McLaren. The 1950s rural young womanhood of the pre-Bucket Hyacinth also features a racially mixed community.

Jason Watkins and Kayode Ewumi in are You Being Served? Photograph: Scott Kershaw/BBC

In the new Porridge, Clement and La Frenais, having gone down the route of Fletcher: The Next But One Generation for their central character, also shadow the classic series in other ways. Dialogue reveals the current whereabouts of the original Fletch and of Lenny Godber, the cellmate played by Richard Beckinsale, while Mr Meekie, a twitchily suspicious Scottish warder, is in name and manner a soundalike for Fulton Mackay as Officer Mackay.

In the tradition of other recent TV prequels such as Young Morse and Rock and Chips (imagining the earlier years of the characters in Only Fools and Horses), Young Hyacinth seeks to show the development of the personality of a later stand-out character. It was clear in Keeping Up Appearances, the BBC1 series that ran from 1990-95, that Patricia Routledge’s Mrs Bucket came from a lower-class family with people and secrets that threatened to embarrass her carefully elevated status. Clarke expands this background – an alcoholic, philandering dad, sisters who mock Hyacinth’s snobbery – in a show in which Kerry Howard has little choice except to impersonate Routledge’s delivery.

In parallel to this BBC1 trio of humour reboots, BBC4 will run new takes on three earlier hit comedies: Hancock’s Half Hour and Steptoe & Son (both written by Ray Galton and Alan Simpson) and Till Death Us Do Part, in which writer Johnny Speight and actor Warren Mitchell gave voice to the bigot Alf Garnett.

It would be interesting to know what staunch West Ham Utd supporter Alf made of the club’s new Olympic-legacy London Stadium, but, although Galton and Simpson are still available at 86, these shows are remakes of original scripts rather than updates. As Alf, Simon Day bravely avoids an imitation of Mitchell, especially the elongated wheedling tone that the formative performer brought to Alf’s it-stands-to-reason speeches. Playing safe, the BBC has chosen an episode that contains none of the racism, which Speight and Mitchell were satirising rather than endorsing, but which would be too high risk for TV today.

Simon Day as Alf Garnett, Lizzie Roper as Else, Sydney Rae White as Rita and Carl Au as Mike as they star in an episode of Till Death Us Do Part. Photograph: Alan Peebles/BBC/PA

As the plot of this Till Death Us Do Part revolves around a public phone box, it will be science fiction for any younger members of the audience who tune in, although it must be questionable that many will. Only Porridge, which has a nice running gag about OCD and neatly incorporates new prison technology such as as electronic door systems, might appeal to someone who didn’t know the old show. Otherwise, Landmark Sitcoms and Lost Sitcoms are essentially tribute band television, in which people who might pass for the originals in a bad light deliver familiar riffs that make you want to get out the originals.

Are you Being Served is on BBC1 on 28 August at 9pm; Porridge is on BBC1 on 28 August at 9.30pm; Till Death Us Do Part is BBC4 on 1 September at 10pm; Young Hyacinth is on BBC1 on 2 September at 9.30pm; Hancock’s Half Hour is on BBC4 on 8 September at 10pm; Steptoe and Son is on BBC4 on 14 September at 10pm