Here is a pure hypothetical:  Suppose that EU regulations miraculously changed/disappeared (e.g. under pressure from the supposed resurgence of the right in the recent elections) to become perfectly amenable to the interests and aims of UK corporations.  Then would the anti-EU rhetoric in the UK media -- at least the part driven and sponsored by UK corporations -- disappear and give way to pro-EU rhetoric?

I think that experiment may have been done in reverse.  IIRC, back when the EU was the EEC,  the Labour Party's then policy to take us out of the EEC was framed by the media as yet more evidence that they were the Loony Left.

So my answer would be-yes, remove all those nasty workers' rights and equality bits and I expect the UK media would have a change of heart.