The early years of Henry VIII's reign was an incipient period for English ciphers. See another article for the earliest English ciphers.
See another article.
A letter from Dr. Magnus (Wikipedia) to Wolsey, Edinburgh, 19 April 1525 (Cotton MS Caligula B VII BL, f.62-66) includes a paragraph in cipher. An incomplete (and partially incorrect) key is attached, and allows reconstruction of the cipher as below. The note in the margin turned out to be an excerpt of the plaintext.

Cotton MS, Vespasian C III and IV include many letters of Edward Lee (Wikipedia), who was sent to the Emperor in Spain in 1525; the Bishop of Worcester (Episcopus Wigorniensis) (Wikipedia), who was sent to the Emperor in Spain in 1526, and Francis Poynts.
While my reconstructions are mainly based on the letters in C III (f.230 (DECODE R8461), f.236 (R8463), f.237 (R8464), f.238 (R8465), f.239 (R8466), f.241 (R8467), f.245 (R8473), f.246 (R8474), f.248 (R8475)), there are many more specimens in C IV.
Cotton MS, Vespasian C IV includes a letter partially in cipher from Sylvester Darius in Spain to Cardinal Wolsey, 5 November 1528 (in Latin) (f.260, DECODE R8589). The letter is calendared in Letters and Papers, iv (British History Online) (in English).
The cipher can be reconstructed as follows.
It appears this is part of a fuller cipher provided with syllables (see the next section).
Cotton MS, Vespasian includes four letters in Latin in which some passages are in cipher:
Vespasian C III f.304 (R8476) Bishop of Worcester, 24 December 1526
Vespasian C IV f.313 (R8589) Bishop of Worcester, 12 February 1529
Vespasian C IV f.315 (R8590) Bishop of Worcester, 15 February 1529, deciphered
Vespasian C IV f.363 (R8613) 22 July 1529
The deciphered fragments allow partial reconstruction of the cipher symbols for syllables in the form of a base letter with a numeral superscript.
This shows the Bishop of Worcester, an Italian absentee, used a more complex cipher in his Latin letters (to Wolsey?) than in his English letters jointly sent with Edward Lee. Use of superscripts in this cipher is better than vowel indicators (i.e., the same number or diacritic always represents the same vowel) used, e.g., in Spanish ciphers in Philip II's time.
Interestingly, single letters that do not form syllables are enciphered in Sylvester Darius' cipher above.
The other three letters, yet undeciphered, also have similar symbol sets and should be in the same cipher.
Cotton MS, Vespasian C IV, f.214 (R8572) is a letter in Latin from a Serno Gilino, 15 September 1527. Most of the superscript numerals of this cipher are two-digit numbers, in contrast to the Bishop of Worcester's above, in which superscripts (at least the meaninful ones) are two-digit numbers. This is not yet deciphered.
Add MS 25114 (BL) includes a letter in cipher from Thomas Cromwell to Gardiner from 26 February 1536, appended to a letter in clear dated 25 February (f.249-252). The plaintext is printed in Roger Bigelow Merriman (1902), Life and Letters of Thomas Cromwell, vol. II, p.5 (Internet Archive, Google) (There is a note of a nineteenth-century(?) archivist on f.250v, dating this letter to 1537.).
The cipher can be reconstructed as follows.

Merriman (1902) prints three letters in cipher from Thomas Cromwell to Sir Thomas Wyatt, who was sent to the court of the Emperor in 1536 (Wikipedia). The originals are in Harley MS 282.
p.113 [no.238] Cromwell to Sir Thomas Wyatt, 11 February 1538 (Harley MSS 282 ff.167, 159) (This letter uses many nulls at the beginning.)
p.122 [no.244] Cromwell to Sir Thomas Wyatt, 1 March 1538 (Harley MSS 282 ff.175-182)
p.140 [no.261] Cromwell to Sir Thomas Wyatt, 10 May 1538 (Harley MSS 282, ff.191, 202)
The cipher can be reconstructed as follows.

According to Garett Mattingly, Renaissance Diplomacy, p.215 (Internet Archive), and Arthurson, "Espionage and Intelligence from the Wars of the Roses to the Reformation", p.150, experts under Thomas Cromwell broke the cipher of the Imperial ambassador, Eustache Chapuys by 1535. I have not been able to identify their sources.
Add MS 32650 (BL) includes a letter mostly in cipher from Sir Ralph Sadler, ambassador to Scotland, to Henry VIII, Edinburgh, 22 April [1543] (ff.214-219).
Add MS 32652 (BL) and Add MS 32653 (BL) include many letters (1543) from Sadler to Henry VIII, Charles Brandon, Duke of Suffolk, Cuthbert Tunstall, Bishop of Durham, or the Privy Council.
Sadler's letters are printed in Arthur Clifford (ed.) (1809), The State Papers and Letters of Sir Ralph Sadler, vol.I (Google), vol.II (Google).
The cipher used in these letters can be reconstructed as follows.

Add MS 32657 (BL), ff. 4r-6v, includes a letter from Sir James Wylford, Governor of Haddington, to William Grey, 13th Baron Grey of Wilton and Lord Lieutenant of the North, dated Haddington, 2 July [1548].
The cipher can be reconstructed as follows.

See another article.
Héder, M ; Megyesi, B. The DECODE Database of Historical Ciphers and Keys: Version 2. In: Dahlke, C; Megyesi, B (eds.) Proceedings of the 5th International Conference on Historical Cryptology HistoCrypt 2022. Linkoping, Sweden : LiU E-Press (2022) pp. 111-114. , 4 p. [pdf]
Megyesi Beáta, Esslinger Bernhard, Fornés Alicia, Kopal Nils, Láng Benedek, Lasry George, Leeuw Karl de, Pettersson Eva, Wacker Arno, Waldispühl Michelle. Decryption of historical manuscripts: the DECRYPT project. CRYPTOLOGIA 44 : 6 pp. 545-559. , 15 p. (2020) [link]
Megyesi, B., Blomqvist, N., and Pettersson, E. (2019) The DECODE Database: Collection of Historical Ciphers and Keys. In Proceedings of the 2nd International Conference on Historical Cryptology. HistoCrypt 2019, June 23-25, 2019, Mons, Belgium. NEALT Proceedings Series 37, Linköping Electronic Press. [pdf]
S. Tomokiyo, "Earliest English Diplomatic Ciphers"
S. Tomokiyo, "Ciphers during the Reign of Queen Elizabeth I"