Why are there so few words in English that are derived from Welsh?
Solution 1:
Language origin specialists theorize that the proportion of loanwords in a language is a function of both the length of exposure to and the social status of the borrowed language.
English words borrowed from Celt are less than one hundred and probably more around 60.
However, the exposure of English to Welsh is long (449 AD to present) but the Welsh language had a lower status from the Saxon point of view.
Remember the double meaning of Wilisc in OE, the Saxon word for Celt (=> Welsh): it means both "foreigner" and "slave" (see the forms Wyel: slave, servant or Wylen: female slave).
Solution 2:
The existing Celtic/Gaelic languages on the British Isles are considerably older than (Modern) English is.
They are native languages to the region. However, when England was first (and repeatedly) conquered (by the Saxons, the Nordic and the Normans), The Celtic regions were avoided and some of the midland natives fled to the extremities (Wales, Scotland, Ireland) and these areas remained largely untroubled by invasion.
There was a time when the districts of England were quite separate and there were many different native languages present (i.e. Manx, Cumbric, Cornish, Salopian). As the different occupations of England came and went, the language united and altered around them. Many of the original languages are now considered extinct.
Going back, you will find periods where the majority of English citizens spoke French and others where they spoke German (an old version of, at least), etcetera; Over time these languages all formed as one.
During these many transformations, the Gaelic and Celtic regions continued rather independently and their distinct languages are a mark of this. It is only in relatively recent times that any real interaction between those and English has occurred and as they have interacted, English has dominated, with the number Gaelic speakers in decline as English language takes over.
(Interestingly though, the Welsh are probably the most zealous in keeping their original languages alive, when compared with the others.)
Therefore, you will see that English, though one of the most widespread languages in the world, is really just a mixed bag of Latin, French, German Greek and old Norse but it is something quite separate from Welsh, Irish and Scottish as those nations were not involved in its political history.
Hope this helps.
Solution 3:
Wales didn't conquer/settle England (well sort of by proxy with Henry Tudor)
There wasn't a great deal of trade or much contact compared to with other countries.
It's art and culture has been a bit more'for consumption on the premises' than Ireland's export of writers and poets.
.... and of course because nobody else can understand or pronounce a word of it ....