Yes, the hub is identical
Same 5x120 PCD and same 72.5 mm centre bore: wheels from Mini Paceman bolt on and centre on BMW 1 Serie F21 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 Paceman is compared with the one from BMW 1 Serie F21 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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6.5Jx16 ET46 · 205/60R16 — Risk of rubbing
Compared with the original 6.5Jx16 ET33 on BMW 1 Serie F21: shock absorber side +13 mm, wheel arch side −13 mm, tyre diameter +5.1 % : fit it with the original tyre size of BMW 1 Serie F21 (195/55R16), not that of Mini Paceman.
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 BMW 1 Serie F21 (M14x1.25), 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 BMW 1 Serie F21 on Mini Paceman?