The old company will get put into liquidation, and shareholders will agree to take shares of equivalent value in the new company.
In UK company law, the governing provisions are in the Insolvency Act 1986, ss.
The sanction of a court is not required (unlike under a so-called "scheme of arrangement", which could or creditors).
Yet if a shareholder objects, he or she may require a cash payment instead of shares.
The purposes can vary, from changing the objects of the business, varying share class rights, or reorganize before a demerger takes place.