3,000 isn't a huge number, especially for a survey that the Guardian is trumpeting as significant, but I think it's statistically enough to be considered a valid snap shot. But the question are a bit odd.
'45% say opportunities for black and Asian people have not got (they mean 'gone') far enough'. What do they mean by opportunities? Opportunities to do what? Unless they explained what they actually meant to each respondent, 3,000 people could be answering 3,000 different questions. Opportunities in education? In the jobs market?
Surveys are useful tools but if the methodology is poor, they are not just useless they are harmful.
Likewise the rise in support for PR. A follow up question could have been why they support it. Brexit? One government in charge for too long? Just a general wish for wider representation of smaller parties?