On Brexit, the polling suggested that adopting a firmer policy position could undermine political support for the party by alienating one group of voters or another.
The Labour frontbench has come under intense pressure to harden its opposition to Britain leaving the European Union or to back a second referendum.
But in the polling, a net balance of 2% of voters said they would be less likely to vote for Labour if it backed a final referendum; 10% if the party backed a “hard Brexit”; and 13% if it backed a “soft Brexit”.