With regards to the unitary patent, a number of questions regarding dual protection arises. First, do the national provisions regarding double patenting under the EPC extend to unitary patents? In Germany, there is a controversial discusion in the doctrine, but a consensus seems to emerge that Article II § 8 IntPatGÜ does not apply to unitary patents, because unitary patents are not "European patents" in the sense of said article. In the UK, similar arguments would seemingly apply to Section 70(2) Patents Act, which also speaks of "European patent" - does this extend to a "European patent with unitary effect"?
Secondly, how should the relationship between "duplicate" unitary and national patents be regulated? The European legislator has not explicitly addressed the issue in Regulation 1257/2012 implementing enhanced cooperation in the area of the creation of unitary patent protection, However, Recital 26 of Regulation 1257/2012 suggests that
Patent applicants should remain free to obtain either a national patent, a European patent with unitary effect, a European patent taking effect in one or more of the Contracting States to the EPC or a European patent with unitary effect validated in addition in one or more other Contracting States to the EPC which are not among the participating Member States.
While the language is not crystal clear, it seems evident that the legislator believes the unitary patent, the EPC "bundle" patent and national patent are alternatives ("either ... or"), i.e., they should not be obtained for the same invention. Recital 26 does not explain anything, but rather orders ("should") that the applicant should chose at the earliest possible time whether to obtain a European "bundle" patent, a European patent with unitary effect or a national patent. It has been argued that such Recitals should have binding effect on the Member States, which seems questionable to me (see also Chudziak in GRUR 2015, 839, 843).
In its proposal for the legislation implementing the Unified Patent Package in Germany, the German Ministry of Justice suggests a compromise: double patenting vis-a-vis unitary patents is not prohibited, but if an action regarding a unitary patent for the same invention is pending before the Unified Patent Court or is made pending during the national proceeding or has been finally adjudicated by the UPC, then the German court will dismiss the action brought based on the national patent insofar as the patents concern the same invention, provided that the defendant raises the objection before the beginning of the oral hearing (see proposed Article 18 Gesetz über internationale Patentübereinkommen, p. 6 of the linked PDF).