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Of British-English origin, the noun sausage roll designates a roll of sausage-meat enveloped in a cover of flour paste, and cooked.

How to make sausage rolls was explained as follows in The Larder and Kitchen for the Month of October, published in The Magazine of Domestic Economy, and Family Review (London, England) of October 1842 [page 174]:

Sausage rolls […] are made by putting the sausage-meat into a light puff paste in the form of a roll, about the thickness of a cucumber, and from four to six inches long. These are baked in a quick oven, and eaten either hot or cold.

These are, in chronological order, the earliest occurrences of the noun sausage roll that I have found:

1-: From Marriages and Deaths, published in The Bury and Norwich Post; Or, Suffolk, Norfolk, Essex, Cambridgeshire, and Ely Advertiser (Bury St Edmunds, Suffolk, England) of Wednesday 20^th September 1809 [page 761, column 2]:

On Monday last T. Ling, aged 75, (an industrious vender of saloop, buns, and sausage rolls) was married to the Widow Bumpstead, aged 42, whom he, no less disinterested than gallant, demanded from her late residence in College-street, vulgarly denominated the Workhouse.

2-: From The Bury and Norwich Post; Or, Suffolk, Norfolk, Essex, Cambridgeshire, and Ely Advertiser (Bury St Edmunds, Suffolk, England) of Wednesday 3^rd June 1812 [page 491, column 1]:

The debtors in the City Gaol return thanks to an unknown benefactor, for a good supper of sausage rolls, on Saturday night.

3-: From the following advertisement, published in The Norfolk Chronicle and Norwich Gazette (Norwich, Norfolk, England) of Saturday 14^th August 1813 [page 2, column 3]:

E. SNELLING,
CONFECTIONER & PASTRY-COOK,
Near the Bull Inn, Magdalen-Street, Norwich,

GRATEFULLY acknowledges the favours of her Friends and the Public, and most respectfully informs them, that she has CONFECTIONARY of all sorts, of the best qualities, Syllabubs, Custards, Blanchmanch, Trifles, and every other requisite for Desserts and Sandwich Parties, will be made to order.
English & Foreign Preserves, Fish Sauces, genuine Spices, Hams and Tongues, on the lowest terms.
Beef Pies, Sausage Rolls, &c. on Saturdays.
An Eating-room for the accommodation of Ladies and Gentlemen.

4-: From The Morning Journal (London, England) of Friday 12^th June 1829 [page 2, column 4]:

We should say—“For God’s sake, and the sake of justice, spare us the infliction of an English jury, and give us the award of a single clear-headed and unprejudiced judge!”
It is monstrous to think that the liberty and property of every man in this country should be at the mercy of twelve persons who, in nine cases out of ten, are swayed in their verdict by one reluctant brother, who, as often happens, may be related either to the plaintiff or defendant, and who, inspired by malignity or hunger, by doggedness or ignorance, wrings from the other eleven a compromise in his favour. Call you this justice, gentlemen of the jury? It is a perversion of justice. It is opposed to common sense and common honesty. It is revolting oppression—it makes equity a word without meaning—it extorts a verdict from the weak, the infirm, the indisposed, and the nervous—it permits the bully or the secret enemy, or him who has eaten the best breakfast, or has lined his pockets with the largest share of sandwiches or sausage-rolls, to dictate to the rest, and level or elevate their opinions to his.

5-: From the following advertisement, published in The Times (London England) of Thursday 1^st March 1832 [page 1, column 1]:

TO the LADIES.—Fine rich WEDDING CAKES, at NORMAN’s, Carlisle-street, Soho-square. The only house in London for the original Scotch bun. A choice variety (fresh daily) of beautiful cakes, suitable for the following purposes—birthdays, christenings, schools, weddings, and funerals; Scotch shortbread, original Banburies, new Brighton Pavilions, sausage rolls, ham sandwiches, and a large assortment of almond routs, buns, pastry biscuits, &c., for the dessert table. Parties supplied with ices, jellies, &c., at low prices. Every article of the best quality. Ladies and gentlemen visiting Soho Bazaar will find the above house convenient to take refreshment. Seed pound cake, very fine.—Carlisle-street, Soho.