Where does the term "tuck shop" come from?

We used to a have a tuck shop at school that sold sausage rolls, pens and pencils etc.

Where does the word come from?

One definition of 'tuck' from The Free Dictionary relates this word to food, which I'm sure we've all heard before:

tuck away/into Informal:

To consume (food) heartily.

Though not definitive, there are two excerpts from Wikipedia worth considering...

• Regarding the origin of 'tuck' in relation to shops:

  The term "tuck", meaning food, is slang and probably originates from such phrases as "to tuck into a meal". It is also closely related to the Australian English word "tucker", also meaning food.

• And, regarding the origin of 'tuck', in itself:

  "Tucker" may originate with the lacework at the top of Nineteenth Century women's dresses, but the origin of its use in regard to food probably arises from the popular shops run in England by various members of the Tuck family between at least 1780 and 1850. The earliest reference found is to one Thomas Tuck whose famous "Tuck's Coffee House" in the university city of Norwich in Norfolk UK attracted many academics.

A tuck shop was originally a pastry shop selling pastries and sweets to schoolchildren.

OED

The Oxford English Dictionary says the verb tuck (often tuck in or tuck into) meaning "to eat heartily or greedily" is from 1810. The simpler sense "to consume or swallow food or drink" is from 1784, and means to ‘put away’, ‘put out of sight’.

Their earliest citation for tuck shop (and tuck as food) is 1857, but I found some earlier examples.

1844

Here's an extract from "A Student's Reminiscences of His Early School Days" (from 1832, at Grey Friars Monastery-Christ's Hospital school in London) in The Student: A Magazine of Theology, Literature, and Science (pusblished 1844, Vol. I):

We passed our time on the two days allowed us in as pleasant a manner as possible ; we had some good games in the field attached to the school, and took great care to spend every farthing of our cash in the "tuck shop," and doubtless were not overglad when we were collected together by one of the beadles and introduced into the grammar-school to have our "divisions" assign us, or to hear which school we were to attend in the afternoon or morning.

1849

Here's an interesting July 1849 from Blackwood's Edinburgh Magazine (Volume 66 - Page 94) that gives a list of some products sold at a Westminster, London tuck-shop:

... we invited several class-fellows to celebrate so remarkable a day at a tuck-shop in the vicinity of Dean's Yard. There, in unrestricted indulgence, did the party get through, there was no telling how many "lady's fingers" tarts, and cheese cakes, and drank - there was no counting the corks of empty ginger beer bottles.

1854

Finally, Edmund Hodgson Yates remembers the list of products available from the baker's next to his old school, in My Haunts and Their Frequenters (1854, Page 98), on the occasion of a visit to the annual prizes day:

Yes, there it stands, and as brightly as ever shines the name of over the door. The "tuck-shop," the baker's next door to the playground, the place where at twelve o'clock dozens of hot ginger-cakes, queen-cakes, and buns were devoured by boys whose dinner-hour was one.