The British-English phrase shipshape and Bristol fashion means in good order, efficiently arranged.

Originally, this phrase was ship shapen and meant arranged properly as things on board ship should be (shapen is the strong past participle of the verb shape, and, used as an adjective, means having a shape of the kind specified by the qualifying word, as in well-shapen).

The word ship shapen is first recorded in The sea-mans dictionary, or, An exposition and demonstration of all the parts and things belonging to a shippe together with an explanation of all the termes and phrases used in the practique of navigation (London, 1644), by the English lawyer, soldier, author, seaman and politician Sir Henry Mainwaring (1587-1653):

(1922 edition)
Rake. The Rake of a ship is so much of her hull as doth overhang both ends of the keel; so that, let fall a perpendicular upon the end of the keel at the setting      on of the stem, so much as is without that forward   on is her rake forward on. And so in the like manner at the setting in of her stern post, and that is her rake aftward on. Commonly the rake forward on is more than a third, but less than one-half of the length of her keel. There is not any one rule observed amongst all nations, for some give long great rakes, as generally all French built; the Flemings not so much. And for the rake aftward on, it being of no use for the ship but only for to make her ship-shapen (as they call it), they give as little as may be, which commonly is about a fourth or fifth part of her rake forward on.
[…]
Wall-reared. That is when a ship is built right up, after she comes to her bearing. This is unsightly, and (as they term it) not ship shapen, but it makes a ship within board much the roomier, and not the less wholesome ship in the sea if her bearing be well laid out.

The expression was extended to Bristol fashion in the early 19^th century when Bristol, a city in south-western England, was the major west-coast port of Britain; the following definitions are from The Sailor’s Word-Book (London, 1867), by the British naval officers William Henry Smyth (1788-1865) and Edward Belcher (1799-1877):

SHIP-SHAPE. In colloquial phrase implies, in a seamanlike manner; as, “That mast is not rigged ship-shape;” “Put her about ship-shape,” &c. (See Bristol-fashion.)
BRISTOL FASHION AND SHIPSHAPE. Said when Bristol was in its palmy commercial days, unannoyed by Liverpool, and its shipping was all in proper good order.

The earliest known instance of the extended form is from Travels of four years and a half in the United States of America; during 1798, 1799, 1800, 1801, and 1802 (London, 1803), by the English author John Davis (1774-1854); Mr. Adams is an American sailor:

Mr. Adams.—My girl lives at Bristol. Was you ever at Bristol?
Passenger.—What Bristol? Bristol in America, or Bristol in England?
Mr. Adams.—Bristol in England. […] I wonder the girls at Bristol don’t take passage for America.
Passenger.—Why?
Mr. Adams.—Why one night I took a sweep of sixty, and cruized a whole watch up Clare-street, down Broad-street, into John-street, to fall in with some ship that had a roving commission, but d—n the single straggler could I find.
Passenger.—Astonishing! I have passed through such a grand fleet of them at Bristol of a night, that I have been obliged to luff up, and bear away, to keep clear of them. Where were they all?
Mr. Adams.—All in a dry Dock! All in Bridewell! Indeed some were outside of the dock-gates; but they were riding the gale out with four anchors ahead; two bowers, a stream and a sheet. It was there I first got alongside of Moll. She is as pretty a girl as ever stepped between the stem and stern of a vessel. And to see her upon a lee-shore! It made me change colour in the face like a dolphin. “My box of diamonds,” says I to the girl, “this is neither ship-shape, nor Bristol fashion.”

The following is from The Times (London) of 23^rd August 1823:

L’Atriveda Spanish privateer, which has been in our harbour several weeks, is now completely refitted in all the graces of “ship shape and Bristol fashion,” and on the point of sailing for whatever chances the fortune of war may bestow.

The Nautical Magazine and Naval Chronicle (London, 1839) published this explanation of the phrase:

“Neither Ship-shape nor Bristol Fashion.”
Nautical proverb.

The renowned city of Briggstowe [= Bristol], the “Place of the Passage,” having recently plucked a feather from the wing of Fame, her hardy sons may be alluded to with a better grace.
The above “saying” current among all British seamen, when they would speak contemptuously of any thing ill put out of hand, evidently implies that, in Bristol things are well done, and by inference that those things appertain to shipping. Commentators appear to have been puzzled in their endeavours to unstrand the lays of this very popular adage. Let us try our hand.
Time out of mind the people of Bristol have been celebrated for their maritime exploits. Cabot, Rodgers, Dampier, Cook, Davis, and other seamen are recorded in the maritime annals, as having sailed out of this port; and her seamen generally were noted for their hardihood, daring, and professional qualifications. During my own experience, I can vouch for those whom I have met with, upholding those qualities; one and all were, what in the service are emphatically styled “prime seamen.”
It is well known that the mariners of this port, were among the foremost to undertake long and perilous voyages, which must have had their influence in perfecting them in the art of seamanship; and hence excelling, is it to be wondered at that they should have obtained by universal consent, a title to the merit of being, if not the first, second to none among their countrymen as excellent seamen? Perhaps, too, self-love may have prompted their own voice in sounding the praise thus awarded them: a compliment, which, whether that be admitted or not, holds good at the present day in the fleet, just as the northern seamen of the east coast of England are, universally, esteemed the best leadsmen.
The point of the compliment thus paid to the tars of Bristol has been used as a sort of oral goad to emulation, the effect of which, however, as a stimulant to exertion, may be supposed to have a different action on the mind of those to whom it is applied, according to their temperament and idiosyncracy [sic]. The present race hold their claim to the character of good seamen, and equally to the local distinction of pugilistic combatancy [sic]!