They are members of the Labour Party, Primrose. This party was always a 'socialist' party and before 1995, Clause IV of the Labour constitution entrenched its socialist values:
“To secure for the workers by hand or by brain the full fruits of their industry and the most equitable distribution thereof that may be possible upon the basis of the common ownership of the means of production, distribution and exchange, and the best obtainable system of popular administration and control of each industry or service.”
On becoming leader Tony Blair changed this. It was agreed by the Labour Party at a special conference in Easter 1995 after a debate that is would become:
“The Labour Party is a democratic socialist party. It believes that by the strength of our common endeavour we achieve more than we achieve alone, so as to create for each of us the means to realise our true potential and for all of us a community in which power, wealth and opportunity are in the hands of the many, not the few, where the rights we enjoy reflect the duties we owe, and where we live together, freely, in a spirit of solidarity, tolerance and respect.”
So now, the Labour party is less socialist. “Social democrats” are usually how more centrist left wing politicians in western democracies are described – and how most Labour MPs would identify. But Corbyn and his allies often use the description: “democratic socialist”.
Ref: New Statesman.