Morrissey and Prince Harry have joined Twitter - so which other celebrities should break their silence (and who should hang up their handles)?

A poll of Independent journalists produced an illustrious list of refuseniks, including Alan Bennett, Baroness Trumpington and George Clooney

Celebrities who we'd like to see on Twitter (clockwise from top left): Tina Fey, Roy Hodgson, the Duchess of Cornwall and Jeremy Paxman (Getty Images)

Ever since, for better or worse, Twitter broke free of the thumbs of its geek inventors to take over the world, celebrities have had three options: a) give in to vanity and the temptation to control one's brand from the get-go; b) resist the pleas of one's agent to get involved until, say, now (and then reserve the right to flounce off after a few hapless tweets); or c) hold out at all costs – to hell with that bloody thing.

This week has seen several comings and goings. The political commentator Matthew Parris announced his departure from Twitter's "turbocharged village pump" on Wednesday. Treading tentatively in the opposite direction came Morrissey, a man not given to brevity (you may remember that the first paragraph of the musician's memoir, published last year, stretched to four and a half pages).

Morrissey, tweeting as @itsmorrissey, a handle he reserved in 2009, opened his account with: "Hello. Testing, 1, 2, 3. Planet Earth, are you there? One can only hope…" At the time of writing, a quarter of a million people had responded by following him. In return, the singer offered a clue as to his motivation for the debut tweet by following back just one account – that of his record label (album out soon!).There was great excitement in some quarters yesterday about another sort-of first tweet, by Prince Harry. The retired helicopter pilot, 29, lent his digital seal to a message for the Invictus Games, an event for wounded soldiers: "Hope everyone will get behind #invictusgames", he tapped into a ceremonial iPad. "Great opportunity to support and thank the men and women who have given so much. Harry."

We can all list prominent tweeters who we might like to do a Parris and leave but who are the celebrities we wish would cease their tiresome resistance and join? A poll of Independent journalists produced an illustrious would-follow list of refuseniks, including Alan Bennett, Baroness Trumpington, who would tweet as @Trumperz, and George Clooney, who once dismissed famous tweeters as "morons" and said he would "rather have a rectal examination on live TV by a fellow with cold hands than have a Facebook page". Steady on, George.

Roy Hodgson, the nervous England manager, was a popular choice. One wit on The Independent's sports desk went so far as to write @Roy3Lions' first tweet, which features a cameo by the now ex-England defender, Ashley Cole: "Just noticed @TheRealAC3 has unfollowed me. Not felt more let down since Vauxhall sent me a Zafira rather than an Insignia #disappointed."

Away from sport, some hoped that Germaine Greer might embrace Twitter's groundswell of new feminism by summarising her damning review this week of Vagenda, the new book inspired by the blog of the same name. Her countryman, the retired cricketer Shane Warne also features in a tweet by @realgreerlovesbeer: "@warne888 y' right cobber, that Vagenda book is only good for the dunny. Another sausage on the Barbie? No worries; best place for 'em."

There is, perhaps, no right way to push oneself into Twitter's harsh light. The Pope kept it real with his opening tweet last year: "Dear friends, I thank you from my heart and I ask you to continue to pray for me. Pope Francis." Ellen Degeneres played the popular, modest "what is this thing" card. "Tis my first twitt-er. Or tweet? Twit? Or tweet? Twit or tweet everybody. Is this anything?" she wrote in 2009, before going on to pick up 29 million followers. Mia Farrow weighed in that same year with the rather worrying: "This is my first tweet. I'm starting a hunger strike on the 27th. Im gonna try to do it for 3 weeks but dont know if I can last that long", which sounds like the inspiration for a new Morrissey song. Stay tuned...

Twitter handles we'd like to see

Alan Bennett @historyboy

Germaine Greer @realgreerlovesbeer

Jeremy Paxman @paxo

Baroness Trumpington @Trumperz

Roy Hodgson @Roy3Lions

Duchess of Cornwall @CamillaSW1A

Bill Murray @noonewilleverbelieveyou

Tina Fey @bossypants

Banksy @OffTheWall

Woody Allen @Sleeper

People we’ve heard enough from

Sally Bercow @SallyBercow

Piers Morgan @piersmorgan

Bret Easton Ellis @BretEastonEllis

Donald Trump @realDonaldTrump

Lord Sugar @Lord_Sugar

Joey Barton @Joey7Barton

Azealia Banks @AZEALIABANKS

Justin Bieber @justinbieber

Jeremy Clarkson @JeremyClarkson

Alain de Botton @alaindebotton