THE DICTIONARY OF PHRASE AND FABLE BY E. COBHAM BREWER
FROM THE NEW AND ENLARGED EDITION OF 1894
"He'll never set the Thames on fire. He'll never make any figure in the world; never plant his footsteps on the sands of time. ... Then, long before our proverb, we had To set the Rhine on fire (Den Rhein anzünden), 1630, and Er hat den Rhein und das Meer angezündet, 1580. There are numerous similar phrases: as He will never set the Liffey on fire; to set the Trent on fire; to set the Humber on fire; etc. ...
I'd also understand "set the Thames on fire" as meaning to achieve something.
But note Roget's Thesaurus:
-- N. bungler; blunderer, blunderhead; marplot, fumbler, lubber, duffer, stick; bad hand, poor hand, poor shot; butterfingers. no conjurer, flat, muff, slow coach, looby, lubber, swab; clod, yokel, awkward squad, blanc-bec; galoot. land lubber; fresh water sailor, fair weather sailor; horse marine; fish out of water, ass in lion's skin, jackdaw in peacock's feathers; quack &c. (deceiver) 548; lord of misrule. sloven, slattern, trapes.
Phr. il n'a pas inventé la poudre; he will never set the Thames on fire; acierta errando; aliquis in omnibus nullus in singulis. "
I suppose there is a vague connection involving being too stupid and boring to be able to achieve anything.