Traditionally, British political parties are regulated only by the electorate, apart from basic rules on matters such as campaign funding which are enforced by the Electoral Commission. There are no rules against discrimination.
You may be interested in these active petitions
It is clear that political parties are not trusted to deal with discrimination themselves. For example, our polling has found that 92% of British Jews feel that UK political parties tolerate antisemitism.
The law should require political parties to have fair, efficient and transparent procedures for tackling discrimination amongst members, or the parties should face substantial fines.
Political parties should be obliged to meet a minimum requirement for tackling discrimination of all forms, including antisemitism, based on the Campaign Against Antisemitism’s guidance at https://antisemitism.uk/politics/manifesto.