The Bell Beaker who lived in Central Europe and were probably the bringers of steppe DNA admixture to Britain and also of Indo-European languages were certainly themselves a synthesis of Neolithic European and Steppe cultures and genetics. They had enough time to become a new people and a new ethnicity, and if the Olalde study was correct then it seems they also had received a significant influence from the non-IE (i.e. lacking steppe components) and pioneer Bell Beakers of Iberia.
Therefore, IMO Central European Bell Beaker was a mixed IE-speaking society and that's what thet brought to Britain, where they of course must've mixed a little more. I don't believe those were the Celts. The Celtic languages, with the exception of clear outliers like Lusitanian and perhaps Ligurian, were too similar to each other to descend from any language older than 1,500 BC. Proto-Celtic is usually estimated to have been spoken in the Unetice cultural period, ~1200 BC.
So, I believe Central Bell Beaker (not Iberian) were Pre-Celtic, and the Celts proper, with their characteristic culture and language, were just the late Unetice and perhaps early Hallstatt, whose ways (and language) were absorbed by similar peoples like the pre-Celtic British. It must've been a bit like the langue d'oïl French "absorbed" the Occitans and the Castillians absorbed the Mozarabs in the last centuries: those cultures didn't disappear, but melted a bit into the more dominant and related culture.