The Wales 1st Dose figure is not that far ahead of that for England 90.3% vs 88.4% - but the gap for second dose is nearer ten percentage points 80.6% vs 71.7%. The main dashboard does not show the age breakdown for Wales, and it would be interesting to compare the older groups' 2nd dose take up. Something less straightforward than it would first appear.
I've taken the latest English 2nd dose uptake from the dashboard, and those for Wales from research.senedd.wales/research-articles/covid-19-vaccination-data/
The English age band calculation uses NIMS; the Welsh uses.....???? - I think the inference is the ONS 2020 based mid year estimate. So not quite apples and apples
The dashboard uses 5 year age bands, aside from aged 90+ and the 18-24 group; the Welsh link starts at 80+; and uses ten year age bands for those under 50. I'm sure PH Wales has more detailed figures but I have not tried to hunt them out (direct links to them gratefully received).
So the graph only really compares the 50-80 age groups; the rest are included but with the caveats above. On those older groups the Welsh uptake is a little higher; not dissimilar to the overall 1st dose gap. I'd expect we'd see the gap in the younger groups narrow as the England 2nd dose roll out continues.
The link to the Wales data (scroll down a fair way has an interesting map showing take up by Welsh council area). The more urban areas, rather like England, lower take up than less urban / rural areas.