UK regional shape map with Scotland, Wales and Northern Ireland

What you really want are Eurostat NUTS Level 1 boundaries, which include UK regions and also the whole of Wales, Scotland and Northern Ireland.

You can fetch the latest 2018 data from UK Office for National Statistics. Depending on your needs, you'll want to choose between generalized (lightweight, but coarse) or full (bigger files with finer detail) geometries. In the latter case, you can also choose between shoreline clipped or full extent (unclipped) geometries.

If I understand the question correctly, you want a shapefile with polygons showing the boundaries for the countries within the UK? You can download one here: https://borders.ukdataservice.ac.uk/easy_download_data.html?data=infuse_ctry_2011

This is from the UK Census data service, you can download a variety of boundaries (electoral, county, district, etc.) at a variety of scales (UK wide, just England, just London, etc). See: https://borders.ukdataservice.ac.uk/easy_download.html

The shapefile download is in BNG which will give you the "typical" UK shape.