What is the relative frequency of English graphemes and/or phonemes in printed UK English texts/spoken English?

I found two resources focused on British spelling that deal with frequency.

The Dictionary of the British English Spelling System (2015) is available through the publisher in PDF for free. It directly tackles the grapheme/phoneme problem and diagrams the possible grapheme combinations for each phoneme. While there isn't a simple list of graphemes in order of frequency, chapter 3 gives frequencies of graphemes for each phoneme in consonants, and chapter 5 does the same for vowels. Meanwhile, chapter 8 gives comprehensive lists of graphemes/phonemes, and Appendix B ("Pedagogically selected lists of phoneme-grapheme and grapheme-phoneme correspondences") is both more accessible and groups phonemes and graphemes according to its "basic" (read: most common) form and its "other" variants.

Then there's this article: Gontijo, P.F.D. et. al., "Grapheme-phoneme probabilities in British English." Behavior Research Methods, Instruments, and Computers 35.1 (2003): 136-157. The article is pretty technical, but its appendix is worth a sit-down over tea: for each grapheme they generated the probability that it would represent a given phoneme. If you just look at the word that it uses as an example, it'll give you a good idea of how each grapheme is used. For instance, "f" is used to represent /f/ about 2/3rds of the time. (The other third of the time it represents /v/, as in "of.")

I hope those help.

From various sources I could find and doing my own calculations, 41% of the letters in British English texts are vowel letters (counting Y in words like "bay" but not in "yard"). The large number of silent vowel letters means that counting phonemes reveal that only 39% of them are vowels. That number appears to be closer to 37% in American English, due to the abundance or rhotics.