The current and historical data on housing completions in England is here:
The latest data tables on housing supply: indicators of new supply.
www.gov.uk
Table 254 gives the house/flat breakdown for completions by region and the percentage splits for houses and flats in 2023/24 are:
England 83/17
London 4/96
South East 71/29
East 80/20
South West 88/12
North West 92/8
West Midlands 94/6
East Midlands 96/4
Yorkshire and Humber 97/3
North East 98/2
Note this has been edited because I didn't read the source table properly, first time I quoted the figures for private enterprise only, missing out housing association properties.
I can't find a more detailed regional breakdown. The East is the region I know best and there will be a huge difference between places like St Albans or Cambridge, where the proportion of flats will be well above 20%, and rural villages in Norfolk or Suffolk, where the proportion of flats will be tiny.
Note these figures are completions in each year not the total housing stock.
The clearest message is that London, the South East and the East are very different from the rest of England.