The adjective joined-up means conjoined. This adjective occurs in particular in the phrase joined-up writing (also joined-up handwriting), which designates cursive handwriting as learnt in elementary school as a stage beyond printing individual letters separately.

The earliest occurrences of the phrases joined-up (hand)writing and to join up writing that I have found are as follows, in chronological order:

1-: From Marie Stopes: Her Work and Play (London: John Bale, Sons & Danielsson, Ltd., June 1933), by Aylmer Maude (1858-1938) [second edition, November 1934, page 130]—the following is about Harry Verdon Stopes-Roe (1924-2014), the son of the British author Marie Stopes (1880-1958):

The way he learned to write is interesting and is sometimes quoted by his mother as an illustration of the ceaseless maternal vigilance needed in the bringing up of children. It was five o’clock in the morning, when he was about five years old, that he sat up in bed and asked for paper and pencil and to be shown how to write “joined up writing so that you can do all the alphabet.” His mother wrote the alphabet in clear copper-plate writing all joined up. The child copied it at once, and that is the only lesson he has had in writing. He writes a good clear round hand approximately like that of a child of eleven or twelve. While other children toil with separate letter formation, an idiotic invention for the destruction of children’s intelligence, he writes whatever comes into his head to write, in a good round running hand.

2-: From Our Merry Comrades Circle. Conducted by Auntie Dick, published in the Mercury and Herald (Northampton, Northamptonshire, England) of Friday 1^st February 1935 [No. 11,208, page 10, column 2]:

My dear Boys and Girls,
[…]
Thank you for your letters and parcels. I had a very heavy Postbag this time, and there was a big entry for the Writing Competition. On the whole the writing was very good indeed. It was clear and upright. I think that the script writing which is taught to the tinies in the schools of to-day is a very good thing. They learn to form really good letters, and so, when they start “joining up” writing it is really very much better than it used to be in my schooldays.

3-: From My Post Bag, in Uncle Jim’s Corner, published in the Hastings and St. Leonards Observer (Hastings, Sussex, England) of Saturday 12^th February 1938 [No. 6,093, page 4, column 6]:

Harold Harris (Hollington) says it takes him a long time to write a letter in “joined-up” writing, and I thank him very much for the letter he sent me.

4-: From Current Topics, by ‘Observer’, published in the Rochdale Observer (Rochdale, Lancashire, England) of Wednesday 14^th August 1940 [No. 7,231, page 2, column 2]:

“Two Charming Little Girls”

In the “Sunday Times” of August 4^th that very entertaining writer “Atticus” mentioned that when Sir Kingsley Wood introduced his Budget there were in the ladies’ galleries of the House of Commons “two charming little girls of such tender years that I wondered if they had mistaken the whole business for the children’s hour.” Last Sunday “Atticus” reported the receipt of the following letter “written in block letters—with none of that silly ‘joined up’ writing—and both in punctuation and condensation it reveals originality and character”:
[Follows a letter written by nine-year-old Sheila Morgan, daughter of Dr. Morgan, Rochdale’s M.P.]

5-: From Uncle Peter’s Postbag, in Uncle Peter’s Children’s Corner, published in the Grimsby Evening Telegraph (Grimsby, Lincolnshire, England) of Saturday 29^th September 1945 [No. 17,697, page 2, column 7]:

Julie Leary (Cleethorpes): “We are back at school now and I am learning to do real writing so I shall soon be able to stop printing my letters to you.”—It’s a big break when you change from printing to joined up writing, isn’t it, Julie? I shall look forward to your letters and I hope you’ll tell me more about your work.

6-: From My Letter Bag, in Aunt Margaret’s Corner, published in The Banbury Guardian (Banbury, Oxfordshire, England) of Thursday 10^th August 1950 [No. 5,506, page 3, column 2]:

Delia Margaret Rodhouse, Dragginton’s Lane, Middleton Cheney.—Thank you very much for my Enrolment Card which I received on my birthday. I had four more cards, a plastic mack, and some money. I shall try to do some of the competitions. I have not learned to do joined up writing yet and I do not use ink at school. So I hope you wont [sic] mind me using a pencil now. I had my school report to-day. I am first out of 37 and I had 250 marks out of 297.

7-: From It Looks Easy for Marian, but…, an article about Marian Hickley, a disabled ten-year-old girl, published in The Evening News and Southern Daily Mail (Portsmouth, Hampshire, England) of Thursday 23^rd April 1953 [No. 23,628, page 3, column 1]:

She is very proud of the fact that she can do everything for herself, wash and dress, even the doing up of those awkward buttons, and also that she has taught herself to do “joined up writing” with her left hand.

8-: From Infants in the Junior School, by R. J. Wells, Green Lanes School, Hatfield, Hertfordshire, published in The New Era in Home and School (London: New Education Fellowship) of December 1958 [Vol. 39, No. 10, page 233, column 1]:

Good writing must be insisted upon from the start, and it does assist the child enormously if he learns to do one style, e.g. not starting in the Infant School printing his letters and then having to change to ‘joined-up’ writing when he reaches the Junior classes.

The phrase joined-up (hand)writing has come to be used humorously to suggest a basic level of intelligence or standard of educational attainment, or, depreciatively, a lack of these. The following, for example, is from Games people slay, about the upcoming Olympic Games, by Barry Norman, published in The Guardian (Manchester, Lancashire, England) of Monday 21^st August 1972 [page 11, column 1]:

The Americans, as usual, will be represented by career college boys, many of whom after no more than a decade at university have the dazzling ability to read simple words without moving their lips and jot down their names in joined-up writing with hardly a spelling mistake.