The key issue here is that Stansted does not have true airside transit for separate tickets. With a self transfer on Ryanair, you’ll have to enter the UK landside and go through Border Control.
Transit Without Visa can apply in some cases, but it depends on your nationality, not just your residence permit. A Schengen residence card alone doesn’t automatically guarantee you can enter the UK visa free.
The UK has specific TWOV rules and they’re very nationality dependent. Some passport holders qualify if they have a valid visa or residence permit from certain countries, others don’t.
Also, Ryanair will go strictly by Timatic at check in. If the system says you need a UK visa to enter, they won’t let you board in Luxembourg.
I would strongly recommend:
Checking the official UK government visa checker using your exact passport nationality
Verifying what Timatic says for your passport + Luxembourg residence permit
Not relying on anecdotal reports
If there’s any doubt, a self transfer at STN is risky because you cannot stay airside.
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