Labour Party’s National Policy Forum was consulting on policy areas for the next manifesto until 24 June 2018. This has now closed. See https://www.policyforum.labour.org.uk/consultation2018
Culture was part of the Environment, Energy and Culture Policy Commission which was tasked with leading Labour’s policy development on the environment, food and rural affairs, energy and climate change, and culture, media and sport.
Nearly all submissions were environment, energy and climate change. It is not clear whether or when the NPF will say about culture and what that might be.
Culture is a matter devolved to the governments in Scotland, Wales and Northern Ireland. In 2017 the culture manifestos in Scotland and Wales very largely mirrored the UK manifesto.