Non-decodable books such as BC&K are tricky because if you know the basic letter sounds e.g. the letter 'a' makes the sound /a/ as in apple, a word where the code is a bit more complex, then you can't fit the letters together into a word. So you CAN read 'cat' but not 'lake' which would sound. But BC&K books contain lots, in fact mostly such words. They rely on the child using the pictures to guess what the word may be, and then recognise the whole word again in a later book. So it is no surprise that he struggled earlier!
It sounds like he has recently 'clicked' with blending, perhaps due to learning at school in his other language - blending is essentially the same process in any alphabetic language. That's great! Sometimes children manage this a bit later, but often once they've 'got it', they start making rapid progress.
Seeing as he can now blend letters (sounds) into words, I'd say it is all the more important to use 'decodable' books to practise reading in English. Levels 1-3 in ORT terms use only very simple phonics, later you start getting split digraphs etc which can be a bit confusing for struggling learners especially if it is their second 'reading language'.
You could use:
Songbirds series by Julia Donaldson (there are often cheap sets on the bookpeople page)
Floppy's phonics, if you want to stay with the BC&K characters
Jelly & Bean
Dandelion (readers/starters; they also have an app that comes highly recommended on MN)
I can also recommend Oxford Reading Owl (online); you can get lots of free, levelled e-books (tick 'phonics books'). Even if you don't want DS to read online, you can use it as a guide for yourself, to find books that he can decode and assess if they might be of interest to him/catch his attention.