As long as the vinyl tiles are stcuk down very well and it sounds like they are, its up to you really. Its not the ideal answer but if you firstly go over the floow with some heavy duty emery or sand paper to give it a bit of a key, then scrub well with sugar soap, you can, when its dry, paint with an undiluted coat of PVA adhesive. Then lay the tiles. See our projects on preparing woodwork for painting to buy the sugar soap, PVA for the adhesive and laying floor tiles for help with this.
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