Starting in Reception with mark making, beginning to form letters in Y1, and built on / practised / reinforced in every school year that follows.
It's part of the UK national curriculum (as a subsection of English) which you can easily find online.
Here is the curriculum extract for Y2:
Statutory requirements
Handwriting
Pupils should be taught to:
ï‚§ form lower-case letters of the correct size relative to one another
ï‚§ start using some of the diagonal and horizontal strokes needed to join letters and understand which letters, when adjacent to one another, are best left unjoined
ï‚§ write capital letters and digits of the correct size, orientation and relationship to one another and to lower case letters
ï‚§ use spacing between words that reflects the size of the letters.
Notes and guidance (non-statutory)
Pupils should revise and practise correct letter formation frequently. They should be
taught to write with a joined style as soon as they can form letters securely with the
correct orientation.
And the extract for Y3:
Statutory requirements
Handwriting
Pupils should be taught to:
ï‚§ use the diagonal and horizontal strokes that are needed to join letters and
understand which letters, when adjacent to one another, are best left unjoined
ï‚§ increase the legibility, consistency and quality of their handwriting [for example, by
ensuring that the downstrokes of letters are parallel and equidistant; that lines of
writing are spaced sufficiently so that the ascenders and descenders of letters do not
touch].
Notes and guidance (non-statutory)
Pupils should be using joined handwriting throughout their independent writing.
Handwriting should continue to be taught, with the aim of increasing the fluency with
which pupils are able to write down what they want to say. This, in turn, will support their composition and spelling.
Some schools follow spelling schemes, some schools don't or have their own.
You could ask for your particular school's handwriting policy or it might be on their website.