[Routine Help] Does a very low percentage of BHA require you to wear sunscreen on cloudy days?

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My toner has Salicylic acid as one of the last few ingredients, but doesn't say how much the percentage is on the bottle. It's a cheap brand and I doubt if it's potent because it hasn't had any drastic results (I've used it for at least 2 months). My question is if I should wear sunscreen because of the BHA even when it's not sunny outside? My location is the UK, if this helps.Edit: I don't use it every day so I'm not exfoliating too much.
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Submitted by sensitive_sloth