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Originally and chiefly used of the River Thames, the British-English phrase silent highway designates a navigable river or canal.

This phrase occurs, for example, in the following from Canals to cut waste paper road trips, by Jessica Rose, published in The Walsall Chronicle (Walsall, Staffordshire, England) of Thursday 25^th July 2002 [page 4, column 5]:

An exciting new project to transport goods by water is to be piloted in Walsall.
Canal boats will be used to collect waste paper and card from local businesses and take it away to be recycled at a Birmingham factory.
[…]
Canal expert Laurence Hogg said the region’s narrow-boats in their industrial heyday moved 335,000 tonnes every day.
He said this was equivalent to 8,000 40-tonne lorries.
“It’s great to see the comeback of our ‘silent highways’.”

These are, in chronological order, the earliest occurrences of the phrase silent highway that I have found:

1-: From A Hand-Book for the Architecture, Tapestries, Paintings, Gardens, & Grounds, of Hampton Court (London: Hugh Cunningham, 1841), by ‘Felix Summerly, Esq.’—i.e., the British civil servant, art patron and educator Henry Cole (1808-1882) [page 7]:

We quite agree with a Westminster Reviewer, who is an excellent guide to Hampton Court, (No. lxvii. page 326,) that the right royal road to Hampton Court is by the “silent highway” of the Thames, which he pleasantly describes from London to Richmond bridge.

2-: From the following title: London. Part I. No. I. The Silent Highway (London: Charles Knight and Co., Wednesday 31^st March 1841), edited by the British author and publisher Charles Knight (1791-1873).

The publication of this first number, and of the following two, was announced as follows in The Patriot (London, England) of Thursday 25^th March 1841 [page 199, column 3]:

London. Nos. I., II., III. Knight and Co., London. 1841.
This work promises to prove a decided hit. It is to appear in weekly numbers, each of which will treat of some distinct feature of the great Babel. For example, the subject of the first is, “the Silent Highway,” alias the Thames; that of the second, “Clean your Honour’s shoes,” or modes of conveyance about London; that of the third, richest in recollections, “Paul’s Cross.”

The following review of London. Part I. No. I. The Silent Highway is from The Northampton Mercury; And Buckingham, Bedford, Hertford, Huntingdon, Cambridge, Rutland, Leicester, Warwick, and Oxford, &c. General Advertiser (Northampton, Northamptonshire, England) of Saturday 3^rd April 1841 [page 4, column 4]:

Under the apt although quaint term “The Silent Highway,” we have a deeply-interesting History of the River Thames—its uses by the ancient Londoners, when it was the common and almost the only highway between Westminster and the Tower Stairs—its pageantries and its sports—its gradual disuse, and the decay of the once powerful and important body of watermen, consequent upon the improvement of the main streets and the introduction of coaches—until the present day, when, by the agency of steam, it has again become a vast thoroughfare for passengers.

3-: From the Morning Advertiser (London, England) of Saturday 3^rd April 1841 [page 3, column 5]:

WATERMEN’S STEAM-PACKET COMPANY.

A new Steam-boat Company has been lately formed under the above title, for the purpose of enabling the watermen of the river Thames to embark, as far as their means will permit, in steam-navigation, which has almost superseded the use of small boats. […]
[…]
[…] What a mighty change has taken place on the “silent highway” of the great metropolis; instead of boats and barges thousands are daily transported from place to place by the means of that powerful agent steam, and the “trim-built wherry” is superseded by handsome gondolas, propelled by steam, for which nothing is found to be too gigantic for its strength, or too minute for its operation.

4-: From an account of the launch of HMS Trafalgar, published in The St. James’s Chronicle, and General Evening Post (London, England) of Tuesday 22^nd June 1841 [page 3, column 2]:

All the world, from her Majesty and her suite down to every cit that could obtain a holiday, flocked yesterday to Woolwich. The roads from London to the dockyard presented early in the day a perfect stream of vehicles, equestrians, and pedestrians, hurrying to the scene of action. […] By water all was bustle, as well as by land. The “silent highway” was as much crowded by steamers and craft of every size and shape as the noisy and very dusty highway on terra firma was by cabs and omnibuses.

5-: From The Globe and Traveller (London, England) of Tuesday 13^th July 1841 [page 3, column 3]:

Wooden Pavement.—The temporary removal of a portion of the fine specimen of wood pavement in Whitehall, for the purpose of laying down gas pipes, at present affords a good opportunity for those who are sceptical as to the merits of this mode of paving to test its durability. It was found on taking up the blocks that their under surfaces and sides were in almost every case as clean and fresh-looking as on the day of their being laid down (upwards of two years ago), and that their upper surfaces had only worn away to the extent of from the sixteenth to the eighth of an inch, notwithstanding the great traffic in this part of the town; the specimen in question is on the Count de Lisle’s plan. When the streets of London shall be generally paved on this principle, the now noisy streets of the metropolis will be almost as much a “silent highway” as father Thames himself.