The English Housing Survey collects data on home ownership in England, broken down by region. This information is detailed in Annex Table 1.2 of the most recent headline report. Figures for the whole of England are detailed in Annex Table 1.1. You can access both tables using this link: https://www.gov.uk/government/statistics/english-housing-survey-2017-to-2018-headline-report
In summary, for the most recent three years of data, the proportion of households in England that were home owners was between 63-64 per cent. The proportion of home owners in the South East for the same period was 68 per cent
We do not hold data on home ownership rates by constituency.