Mr Bell may be interested to learnt that "toffs" is an abbreviation of toffee-nosed person, a term arising when snuff was the favoured "stimulant" used by the very rich; the ones who could afford the many varieties and strengths of snuff.
As a pinch of snuff was inhaled into nostril, and because dribbling noses are not uncommon in winter, it appeared as if toffee was falling from the nostrils of the partakers of this "drug" - the rich upper class
- Getting up to snuff on why toffs are so called, Lord Clifford of Chudleigh, Letters, Western Morning News, October 13 2009
Picturesque an image though this is, I'm of the opinion that it's complete bilge. As this Guardian review says, this etymology for the terms appears in Ian Kelly's 2006 biography Beau Brummell, The Ultimate Dandy -
... the origin appears to derive from the unsightly brown droplets that dripped from a gentleman's nose after taking snuff - which of course was only taken by the "upper class"
- but I'll believe that when I see a contemporary source. And that's the key point with origin stories: it's not sufficient that they be plausible; you have to find evidence of their formation. As far as I can find, there's no sign of anyone using the terms historically to refer to snuff-taking (if this usage existed, you'd expect to find it in descriptions such as A pinch of snuff, anecdotes of snuff taking, with the moral and physical effects of snuff, by Dean Snift of Brazen-nose, Benson Earle Hill, 1840).
In fact the evidence is that "toff" predates "toffee-nosed", and neither of the terms are very old. The Oxford English Dictionary's first citation for "toff" is 1851, in Mayhew's London Labour and the London Poor (it appears in the account of crossing-sweepers of how they solicit money from customers - here). The most likely etymology according to the OED is from "tuft", a term for upper-crust Oxbridge undergraduates, who distinguished themselves from the hoi polloi by wearing a gold tuft or tassel on their college caps. The pseudonymous 1854 college novel The Adventures of Mr Verdant Green - see Wikipedia - has a footnote
As "Tufts" and "Tuft-hunters" have become "household words," it is perhaps needless to tell any one that the gold tassel is the distinguishing mark of a nobleman.
John Camden Hotten's 1874 Slang dictionary: etymological, historical, and anecdotal explains "tuft-hunter" as being a social hanger-on who seeks the society of the wealthy. Hotten also has a significant entry for those who might think "tuft" to "toff" an unlikely jump; he lists an intermediate form "toft"
Toft, a showy individual, a swell, a person who, in a Yorkshireman's vocabulary, would be termed "uppish"
On to "toffee-nosed". The OED's first citation for this is 1943.
Toffee-nose, another of the expressions chiefly heard amongst the W.A.A.F. This refers to a snob or someone who considers herself ‘superior’. It is very apt since it implies that the nose is kept high to prevent it coming into contact with the mouth.
- Service Slang, John Leslie Hunt, A. G. Pringle, 1943
"Toffee-nosed", then, is "toffy-nosed": having the nose of a toff. The description "the nose is kept high" evidently refers to body language - the stereotypical nose-high posture indicating contempt for the lower orders - rather than any toffee-like nasal exudation.
Of course, etymologies are always open to question, and things may not be so clear-cut. Nevertheless, the chronology at least is readily verifiable using Google Books. I can find no pre 20th century uses of "toffee-nosed" (or "toffy-nosed" or "toffee nose"). Here's the search for the range 1600-1900: nothing, except three false positives from dodgy metadata. I couldn't resist, however, trying to pre-date the OED 1943 citation, which seemed a bit late, and the earliest example I can find is in a 1914 edition of Punch, where a cartoon features the aftermath of a fight between Boy Scots, with the caption:
The Victor (after being admonished for un-scoutlike behaviour). "Well, you may say what you like, Sir, but I consider it distinctly subversive of discipline for an ordinary private to call his patrol-leader 'Toffee-nose.'
- Punch or the London Charivari, Vol. 147, December 2, 1914. Project Gutenberg.
A 1921 Notes & Queries lists "toffee-nosed" as trenches slang equivalent to "stuck up". Nevertheless, it chiefly kicked off during World War II, evidently still rooted in military slang:
A premature 'life' will do more to disgust the select and superior people (the RAF call them the 'toffee-nosed') than anything.
- The Letters of TE Lawrence, Thomas Edward Lawrence, ed. David Garnett, 1939
They're county people, all frightfully toffee-nosed and Poona.
- Pastoral, Nevil Shute, 1944
"You wouldn't know a gentleman if you was ter see one, you toffy-nosed coot!"
- Tinned soldier: a personal record, 1919-1926, Alec Dixon
For various reasons, tracking "toff" via Google Books gets into a mess of metadata and indexing problems. Firstly, a search gives many false positives on the German word "Stoff" in Fraktur typeface, so a good start is to limit the search to English texts. Secondly, as you go into older and older texts, you find results increasingly contaminated by mishits on words vaguely resembling "toff" or "toffs" (such as love, Topp, taff, feoff, Tait's, and so on), making it very difficult to search for occurrences in the pre-1851 slot of interest. I don't know what this means about the digitising/indexing process; it happens with the Times Digital Archive and the British Library Nineteenth Century Newspapers database too. Mishits for "toffs", a species of fragrant thistle, are another sidetrack. Once you get to the late 1800s - see search results for 1870-1900 - the false hits clear up, and the results at least show "toff" appears several decades before "toffee-nosed".
So, no luck with beating the OED on "toff" citations. Still, I found a spectacular Google Books metadata crash en route: this hit whose metadata is for the 1845 Archäologische Aufsätze by Otto Jahn, but whose text is Theodore Watts-Dunton's 1898 novel Aylwin. I also found a lovely Melbourne Punch article for September 3rd 1868, Toffs, which leads with spoof etymologies into a taxonomy of varieties of toff as exotic creatures.