With any dealers (not just Peugeot), vague answers and / or a lack of a tracking number that you can check progress online usually means that the dealership is still awaiting build allocations and has not yet placed the order. This issue crops up on this forum continuously.
When we think we have ordered a car we haven’t. We’ve just done the Motability admin. The actual order is placed later between the dealership and manufacturer (entirely separate to the ‘order’ showing on the Motability system, which isn’t an order at all). If dealers have available build slots this can be done the same day or within a day or so. If there are no available build slots it can be a month (or several months) until the order is actually placed. Dealers are almost never honest about this as they don’t want you to go elsewhere.