Personally, I tend to agree with the sentiment conveyed by the YouGov poll.
People living here legally with a confirmed right of permanent residence should have equal access to services and facilities here, regardless of whether or not someone has taken British citizenship.
The association of "entitlement" on the basis of nationality is divisive. A foreign resident living here who retains the nationality of their country of birth can potentially be more of a contributor to society than a British-born resident so it is wrong in principle to limit that person's access to the benefits that should attach to being part of British society.
However, this is entirely different from the question of whether or not as many immigrants as are currently coming into the country should be allowed to settle here in the first place.