I have not worked on mesh-less methods, but in VOF scheme for simulation of interface between two phase with high difference of density, usually there is same problem, the most important reason that I have found was the errors in advection of momentum in interface. The Concept in papers of Rudman can help you, Also I have a paper about it.

I think other reasons such as surface tension is not the main.

 https://www.researchgate.net/publication/265270475_A_New_Method_in_Two_Phase_Flow_Modeling_of_a_Non-Uniform_Grid

Article A New Method in Two Phase Flow Modeling of a Non-Uniform Grid

As Asghar, I do not have work on mesh-less methods but this problem sounds me familiar but for the problem of two-layer shallow water models. If two layer model is solve independently for each layer, spurious oscillations may appear. It is absolutely necessary to treat the problem as a coupled system in order to avoid the appearance of these spurious oscillations. A reference where this problem is treated in the framework of two-layer shallow water systems is Castro, Macías, Parés (2001)

Article A Q-scheme for a class of systems of coupled conservation la...

This issue can be seen and many approaches. I do not work with meshless, but It can be some related to your approach, As our friends have mentioned, you will find this problem in  many schemes. And  the techniques used to circumvent it. Some methods a sensible to mesh,  time step, for example. In meshless I do not have in mind what can generate spurious velocities. 

I have not worked on meshless method and am not sure what exactly it is. Spurious currents have been shown to be generated due to inappropriate evaluation of curvature as well normal vector in the surface tension force calculation. The balanced-force-algorithm eliminate the spurious currents to a great extent if the interface curvature is accurately calculated. The curvature calculation based on height function is a second order method and works very well if the interface is properly resolved. The combination of height function and balanced-force-algorithm give excellent results even in the vicinity of the wall. This method is also very easy to implement.

In my point of view, the height function (Proposed by Ashgriz et. al.) is an artificial method although it could solve some part of the problem.

Hi,

How difficult is it to reduce these currents in OpenFOAM where the reconstruction methods using PLIC are not implemented.

OF uses another scheme named "interfaceCompression" in order to develop a sharp bounded interface rather. Though interface is sharp spurious current at interface surface survive. Any alternative options please.