The phrase the gnomes of Zurich denotes the international bankers and financiers, especially those associated with Swiss banking, regarded as having secret or sinister influence in financial matters.

The earliest instance that I have found is from the column Inside Canada, by Godfrey Hodgson, in The Observer (London) of 24^th June 1962—the author wrote the following about “the intimate connection—many Canadians would say subjection—of the economy to that of the United States”:

Speculation against the Canadian dollar can happen without the malicious gnomes of Zurich as U.S. head offices take normal decisions about the cash flow inside their own business.

This phrase is generally said to owe its origin to a speech that the British Labour statesman Harold Wilson (1916-95), then Shadow Chancellor of the Exchequer, delivered at the House of Commons on 12^th November 1956:

Traders and financiers all over the world had been listening to the Chancellor. For months he had said that if he could not stop the wage claims, the ​ country was “facing disaster”. Those were his own words.
Rightly or wrongly these people believed him. For them, 5^th September—the day that the Trades Union Congress unanimously rejected the policy of wage restraint—marked the end of an era. And all these financiers, all the little gnomes in Zurich and the other financial centres about whom we keep on hearing, started to make their dispositions in regard to sterling.

However, Lord Balfour of Burleigh had already used the image on 7^th March 1956 during a debate at the House of Lords on the economic situation:

My noble friend Lord Clitheroe talked about psychology being important. A noble Lord opposite shakes his head. Let me refer him to the Manchester Guardian of to-day. This is a quotation from the financial correspondent of the Manchester Guardian, which says:
“A curiously unequal struggle is going on in the exchange market. On the one side are foreign speculators, a small but extremely powerful band of European financial interests. These are the ‘little gnomes sitting over ticker tapes in Zurich.’”…“The little gnomes”—
Noble Lords on this side of the House will be interested to hear this—
“are men of extremely conservative opinion. They long ago decided that the present British Government would be unable to maintain the exchange value of sterling. In their view, the Government’s fear of creating unemployment will stop it from breaking the spiral in wages and prices, and sooner or later another devaluation of sterling will be inevitable. From time to time they decide that devaluation is imminent and a skirmish develops in the foreign exchange market.”

The following is the original text quoted by Lord Balfour, from Skirmish in Sterling, published in the Manchester Guardian (Manchester, Lancashire) of 7^th March 1956:

A curiously unequal struggle is going on in the foreign exchange market. On the one side are foreign speculators, a small but extremely powerful band of European financial interests. These are the “little gnomes sitting over ticker tapes in Zurich.” On the other side is the British Treasury’s exchange equalisation account. The struggle is unequal because the account, though an extremely powerful force, is at present absent from the fight. The London market is left defenceless. No British private individuals or bankers are permitted to take a speculative position in currency and the foreign speculators call the tune. They were again victorious yesterday when sterling fell a further 3-16 cents to United States $2.80 7-32, making a fall of 21-32 cents since Friday.
The “little gnomes” are men of extremely conservative opinion. They long ago decided that the present British Government would be unable to maintain the exchange value of sterling. In their view, the Government’s fear of creating unemployment will stop it from breaking the spiral in wages and prices, and sooner or later another devaluation of sterling will be inevitable. From time to time they decide that devaluation is imminent and a skirmish develops in the foreign exchange market.

In the Manchester Guardian’s article, therefore, the clause little gnomes sitting over ticker tapes in Zurich is in quotation marks, which seems to imply that the author is citing someone else. I have unfortunately not found who that was.

However, that clause might simply be a reference to an image already used in The Observer (London) of 30^th October 1955, in which the political correspondent reported on a speech made in the House of Commons by the British Labour politician Hugh Gaitskell (1906-63), then Shadow Chancellor of the Exchequer—the British Conservative politician Richard Austen Butler (1902-82) was then Chancellor of the Exchequer:

The audience that listened to Mr Gaitskell was not confined to the public galleries of the House of Commons or the Conservative and Socialist benches. It included all those clever little financial gnomes, sitting by their tape-machines in Zurich and Paris and Amsterdam and New York.
What will they make of Mr Gaitskell’s charge that Mr Butler is a confidence trickster? That he is without a fig-leaf of integrity? That he will betray his country for the bauble of office? Above all, what will they think as the read and, no doubt, underline—Mr Gaitskell’s blessing on present and future wage claims? What will the unions make of it? In other words, the danger of the situation is that Mr Gaitskell and the Labour Party may, for political reasons, create a financial crisis that can be cured only by draconian measures.