I hypothesize that the different forms for berry are a consequence of English and Germanic languages' tendency to form compounds at a higher rate, specifically with the word berry, a tendency that didn't make its way into Latin or Italian.
Berry comes from Germanic languages
Berry is a word inherited from Germanic (OED, "berry, n.1"). The full etymology uncovers cognates and predecessors in a number of Germanic languages:
Found, with some variety of form, in all the Germanic languages: with Old English bęrie weak feminine, compare Old Norse ber (Danish bær , Swedish bär ), Old Saxon beri (in wîn-beri ), Middle Dutch bēre , Old High German beri strong neuter, Middle High German ber and bere neuter and feminine, modern German beere feminine. These point to an Old German *bazjo-m , as a byform of *basjo-m , whence Gothic basi neuter (in weina-basi ‘grape’). The s type is also preserved in Middle Dutch beze , modern Dutch bes , also Middle Dutch and modern Dutch bezie feminine. The feminine forms Dutch bēzie and Old English berie answer to a Germanic extended form *basjôn- , *bazjôn- . The ulterior history is uncertain: *bazjo- has been conjecturally referred to *bazo-z bare adj., adv., and n., as if a bare or uncovered fruit, also to the root represented by Sanskrit bhas- to eat.
I understand the Italian word for berry to be bacca (Vocabolario Treccani), which comes from the Latin baca (Wiktionary). So berry and baca share a different point of origin at least a couple of thousand years back. Having a different origin doesn't have to result in a different form: plum comes through Germanic but retains an indirect relationship with the Latin pruna (OED, "plum, n. and adj.2"). But one tendency in Germanic does come into play in this case to produce forms distinct between English and Italian: forming words through compounds.
English and more specifically berry loves to form compounds
Latin, Italian, and English all have processes for forming words through compounds. However, only English formed many compounds out of the word berry. Latin did not form compounds for its different berries to connect berries morphologically. Instead, the Latin/Italian names each have different origins. For instance, mirtillo is related to a Greek word for myrtle, from Semitic (Wiktionary); mora is related to the Greek word for black mulberry or blackberry, whose form goes right back to proto-Indo-European (Wiktionary). Baca did not generate many compounds, including for any of the berries you list.
However, berry did generate several compounds in English, including at least one (strawberry) that doesn't appear in other Germanic languages. (German uses Erdbeere, Dutch aardbei, Danish jordbær, each compounding but not with a cognate of straw (Wiktionary).) English has many other berries as well: gooseberry, bilberry, mulberry, crowberry, barberry, bearberry, hag-berry, dingleberry, elderberry, and still others. The prevalence of the compound for berry in English is no surprise; linguist Ingo Plag commented that compounding is "the most productive type of word-formation process in English" (Word-Formation in English, p. 131; Google Books). While Latin occasionally deigns to form compounds, English does it all the time, from Old English onward. So do other Germanic languages. To use Dutch alongside English using the chart from the question, you can see the general tendency to using a compound form in a Germanic language:
Dutch |
English |
Aardbei |
Strawberry |
Bosbes |
Blueberry |
Veenbes |
Cranberry |
Framboos |
Raspberry |
Braambes (Braam) |
Blackberry |
So you can see at least a linguistic tendency in English to form compounds with berry that is absent in Italian.1 In the last section, I'll consider the geographic implications of the question: is this about the difference between fruit availability in southern and northern Europe?
Considering the geography hypothesis again
Your guess is that indigenous plants in England would share an English or Germanic origin, whereas plants introduced to England would share a Latin origin. That is possible, especially with lemon, orange, apricot, and peach, and possibly with other fruits.
There are exceptions. Mulberry shows that a fruit from outside England can be adopted as a berry anyway. Varieties of the mulberry tree (Latin morum, Italian gelso) have origins in South Asia and are widely grown in southern Europe, northern Africa, the Middle East, and India (Wikipedia). Mulberries perhaps came to England during the Roman period (Morus Londinium). Old English did have a word, more, used to refer to a mulberry tree ("more, n.2"). However, mulberry occurs in English by the 14th century anyway and replaces more; the mul- in mulberry probably comes from Latin morum, but now as a compound with berry (OED, "mulberry, n. and adj."). So English could take a very old fruit by another name and berry it.
Mulberry could be compared to pear, which was also an import whose name comes from Latin. Where more was entirely replaced by mulberry, pear has remained relatively stable in form. Perhaps berry specifically tends to form compounds for anything that is a berry or berry-like, whereas the compound options for non-berry fruit are more limited (e.g., pearfruit, which is occasionally used to differentiate fruit from tree but does not replace pear).
So I can't completely answer the geographical question, but I would guess that berry being particularly prone to compounding in English explains at least part of the difference in forms. That makes the geography hypothesis harder to test.
1 Beyond the scope of this answer are other food compounds. For instance, does nut behave similarly to berry? Hazelnut is nocciola in Italian. Walnut is simply noce or nut. Chestnut is castagno/a. If someone wanted to do a more complete study of food geography and etymology, I would recommend looking at other compounds.