I have an old bureau which has several areas where the veneer is peeling off and missing - can I remove it all as it is past fixing and if so how do I take it off and how should I treat the wood underneath thank you

Try a 4" razor scraper on that verneer. Carefully keep the scraper between the verneer and the base wood, short strokes and taps with a hammer. The wood under the verneer will not be very nice so plan to paint or re-apply a verneer. You should sand the base wood until smooth and flat before paint/verneer.