Yes, the hub is identical
Same 4x100 PCD and same 56.1 mm centre bore: wheels from Mini Coupe bolt on and centre on Peugeot iON without rings. You still need to check the offset and tyres, detailed below.
≈: width estimated from the original tyre size.
Wheel by wheel: offset and tyres
Each original wheel from Mini Coupe is compared with the one from Peugeot iON of the same diameter: how much closer the wheel gets to the shock absorber or how far it sticks out of the wheel arch, and whether the tyre keeps the same overall diameter.
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5.5Jx15 ET45 · 175/65R15 — Risk of rubbing
Compared with the original 4Jx15 ET35 on Peugeot iON: shock absorber side +29.1 mm, wheel arch side +9.1 mm, tyre diameter +6.8 % : fit it with the original tyre size of Peugeot iON (145/65R15), not that of Mini Coupe.
Check in detail
Before fitting the wheels
An identical hub is not enough: offset, width and diameter change the position of the wheel, and larger calipers can touch a smaller wheel. Original wheels often use bolts or nuts with a specific seat: keep the fixings intended for the wheel, with the thread of Peugeot iON (Ecrous - 12x1.50), tightened to the torque shown on its vehicle page. Finally, check that the size is among the approved fitments for your vehicle. This comparison is for guidance only: have the fitting approved by a professional.
And the other way round: wheels from Peugeot iON on Mini Coupe?