We consistently obtained significantly positive f4 statistics, implying that both the modern Celtic samples and the ancient Saxon samples have more Steppe ancestry than the modern Anglo-Saxon samples from southern and eastern England. This indicates that southern and eastern England is not exclusively a genetic mix of Celts and Saxons.Southeastern England is genetically very homogeneous. If the people there were a mix of ancient Celts and Saxons you'd expect them to be intermediate between modern Celts (who should have more Celtic ancestry than the modern English) and ancient Saxons (who should have more Saxon ancestry than the modern English).
But, it seems that the English have less steppe ancestry than both modern Celts and ancient Saxons, so they're not really intermediate. My guess is that the English have Norman ancestry that the Celts don't. While the original Normans were Scandinavians with presumably lots of steppe ancestry, I'd be surprised if the post-1066 Normans that settled England were not already heavily admixed with the "French" and so had less steppe ancestry than the modern British Celts from Wales and Scotland.
Population structure of UK Biobank and ancient Eurasians reveals adaptation at genes influencing blood pressure
Kevin Galinsky et al.
Analyzing genetic differences between closely related populations can be a powerful way to detect recent adaptation. The very large sample size of the UK Biobank is ideal for detecting selection using population differentiation, and enables an analysis of UK population structure at fine resolution. In analyses of 113,851 UK Biobank samples, population structure in the UK is dominated by 5 principal components (PCs) spanning 6 clusters: Northern Ireland, Scotland, northern England, southern England, and two Welsh clusters. Analyses with ancient Eurasians show that populations in the northern UK have higher levels of Steppe ancestry, and that UK population structure cannot be explained as a simple mixture of Celts and Saxons. A scan for unusual population differentiation along top PCs identified a genome-wide significant signal of selection at the coding variant rs601338 in FUT2 (p=9.16×10-9). In addition, by combining evidence of unusual differentiation within the UK with evidence from ancient Eurasians, we identified new genome-wide significant (p less than 5×10-8) signals of recent selection at two additional loci: CYP1A2/CSK and F12. We detected strong associations to diastolic blood pressure in the UK Biobank for the variants with new selection signals at CYP1A2/CSK (p=1.10×10-19)) and for variants with ancient Eurasian selection signals in the ATXN2/SH2B3 locus (p=8.00×10-33), implicating recent adaptation related to blood pressure.