The new paper, Large-scale migration into Britain during the Middle to Late Bronze Age, did not resolve the origin of the Celts. But one thing I was curious about:
Evidence for a substantial contribution from the C/EBA population to later populations also comes from Y chromosome haplogroup R1b-P312/L21/M529 (R1b1a1a2a1a2c1), which is present at 89±5% in sampled individuals from C/EBA Britain and is nearly absent in available ancient DNA data from C/EBA Europe (Supplementary Table 9). The haplogroup remained more common in Britain than in continental Europe in every later period, and continues to be a distinctive feature of the British isles as its frequency in Britain and Ireland today (14-71% depending on region19) is far higher than anywhere else in continental Europe (Extended Data Fig. 5).
If you go online you can see the frequency of R1b-L21 varies a lot in England, with rather low frequencies in East Anglia, and higher fractions in western Britain. In Ireland, the frequencies may exceed 80% in the western counties. Lara Cassidy noticed early on that the Rathlin sample from Bronze Age Ireland, an a Bell Beaker individual, carries this mutation. On the continent, the mutation is found in Brittany, subject to migration from Britons, while in Spain it seems to be found in lower frequencies, mostly in the western provinces.
One of the insights of the new paper above is that there seems to have been an Urnfield-related migration that arrived in England around ~1200 BC. Did they bring Celtic speech? I think they were Brythonic and P-Celtic speakers. I believe that R1b-L21 and the Bell Beakers brought Goidelic Q-Celtic languages, and there are some who argue that Celtiberian was a Q-Celtic language.