Your best practice way of prepping that floor for sheet vinyl would be to remove the tiles and the underlayment (hardboard?) down to the bare T&G floorboards. Your bodge suggestion will fail in months.
Vinyl needs to be laid on a smooth, firmly fixed, sheet of 12mm ply for instance.
Best practice further suggests that you first remove the WC and Pedestal before any prepping - in fact, fwiw, the room should have been a shell (no bath either) before starting.
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