Is it Labour? No. Since Blair, Labour are no longer a real party for labour interests in the UK. They still take donations from the unions, but that doesn’t make them “for” labour interests. Or even “for” social justice.
The LibDems? Never were. And that’s before they got into bed with the Tories.
Nope. If you want a party which has a commitment to social justice written into its constitution, you need the Green party. So: for social justice, you need to be supporting the party which polled 7th in the popular vote at the last general election – a number skewed rather high as the Greens fields nearly 10 times as many candidates than any of the 8th through 12th largest parties.
This is our representative for social justice in mainstream politics. And people wonder why we young people lose faith in mainstream politics.