From the latest suggestions/some I missed.
If it helps, the person I'm desperately trying to think of has /had a good head of hair, and whilst I see him with a moustache, there's no beard. Hair is quite full with a bit of bouffant/wave. I think reasonably tall but not excessively so. Quite 'portly' but not exactly fat.
I think he'd have been in things when he was in his later 50s but I'm not good with ages. And that would have been in the 1990s or early 2000s, maybe just a bit later.
Peter Ustinov
Already mentioned. Looks superficially similar as Poirot but not him
Clive Mantle
No. Face is a bit too shapely around the jaw, hairline too high, face too thin
Martin Shaw
No. Not one of the Professionals. Martin is too well-known
Nigel Stock
Not really like him at all. Hair whiter, face longer and more rectangular
Richard Durden
No. Wasn't in Ghosts. The mouth is a bit similar but again, forehead too high, hair not white enough.
Danny Webb
No. Face is wrong shape, hair is not the right colour, hairline too high, eyes too 'baggy'
Trevor Eve
No, not Shoestring. He's got too much of a defined chin, too neat a beard. I don’t think my person has a beard.
Derek Jacobi
No. Nowhere near as famous
Michael Cochrane
No. Hairline too high, eyebrows look too thin/sparse
Frank Muir
No. Just not him. Not someone who could wax lyrical on panel shows/radio shows. And I think too old too.
Frankie Howerd
No. Not any sort of raconteur or comedian as far as I can recall
Wilfrid Hyde-White
No. Possibly too old. Chin/neck too defined, no facial hair, and hair wrong
Richard Attenborough
No. Not that famous.
Charles Laughton
No. Doesn't look anything like him and too old.
Alfred Hitchcock
No.Too bald, hair wrong colour. I see him as quite short. Also, I think, too old.
Michael McKean
Possibly the right sort of age but not him. Hairline possibly similar.
Brewster Mason
No, but possibly similar around the eyes/nose
Marty Feldman
Just no.
James Robertson
I can't find anyone with that name - only James Robertson Justice. His hair is the wrong colour, and face a bit too oval.
Keith Barron
No. I thought already mentioned but possibly similar hair (albeit white ) when Keith was in Duty Free
Conleth Hill
No. Hair is wrong although face shape across the cheeks looks vaguely similar to the person I'm thinking of
Patrick McGoohan
No. Not the Prisoner
Charles Dance
No. Not as well known. The person I'm trying to think of is possibly a bit older
Ivor Danvers
No, face shape wrong. Hairline too high
Robert Daws
No. Hariline too high, and I think too young.
John Gielgud
No. Too famous
Tom Courtenay
No. Might be the right sort of age. But again, too well known
Kenneth Branagh
No. Too famous, too young
Alan Bates
No. Hair too dark, and too conventionally handsome
George Cole
No, but some vague facial similarities around the mouth and eyes
Gordon Jackson
Too ginger, too obviously scottish. Hairline too high, face wrong shape.
David Warner
No. Hair is wrong and he's too thin
Richard Bradford / John Challis / Michael Gambon /Nicholas Farrell / Philip Jackson / David Suchet / Anton Rogers / Donald Sutherland / Malcolm McDowell / Terrence Alexander / Terrence Stamp / Denholm Elliott
Again, not someone who would be playing a main character and I don't recall any particular accent. Going back to the 'fastidious' idea - I get the impression of maybe a fob watch or a gold pinky ring type person, which again would tie into a character actor in an Agatha Christie type (but not absolutely that) thing.
I think this is someone who'd probably be in their late 70s or early 80s by now, maybe even a bit older, if they're still alive.