I think police should be able to lie, but any response to a lie should be presumed a lie by the justice system. So, a lie can be used to get an undercover cop out of trouble, but a lie cannot help an interrogation.
Essentially, an officer of the law deciding to lie should invalidate all evidence gained after the lie.
Two thoughts. First, should undercover investigations be allowed? Should law enforcement officials be allowed to lie about their identity in order to obtain more evidence? It is not a trivial question, although I agree with you that we don't need secret police.
Second, does simply saying that public servants aren't allowed to lie...work? It seems like there are many situations where public officials lie broadly and baldly, and there is no comeuppance, not even when perjurious!