Refer to figure.
When visibility is reduced below VFR minima inside controlled airspace like a CTR (Control Zone), a Special VFR clearance is required to enter and operate under VFR conditions. Since the ATIS reports visibility of 4000 meters, which according to the table, is below the required VFR minima for all airspace classes, a Special VFR clearance is necessary before entering the CTR.

SERA.5005 Visual flight rules

(a) Except when operating as a special VFR flight, VFR flights shall be conducted so that the aircraft is flown in conditions of visibility and distance from clouds equal to or greater than those specified in Table S5-1 (attached figure).

Standardised European Rules of the Air (SERA)
SERA.8020 Adherence to flight plan

(d) Weather deterioration below the VMC. When it becomes evident that flight in VMC in accordance with its current flight plan will not be practicable, a VFR flight operated as a controlled flight shall:

(1) request an amended clearance enabling the aircraft to continue in VMC to destination or to an alternative aerodrome, or to leave the airspace within which an ATC clearance is required; or
(2) if no clearance in accordance with a) can be obtained, continue to operate in VMC and notify the appropriate ATC unit of the action being taken either to leave the airspace concerned or to land at the nearest suitable aerodrome; or
(3) if operated within a control zone, request authorisation to operate as a special VFR flight; or
(4) request clearance to operate in accordance with the instrument flight rules