If you overstay in one country, most or all other countries will worry about you overstaying in their country as well.
Because of that your overstay is going to hurt your chances on a visa in other countries.
When countries share information your overstay will be known whether you mention it or not, but even if they do not share information they will mostly ask you about bans.
On the other hand, if you can proof that your ban was due to an overstay of only one day and your ties to your home country are strong, the immigration officer who handles your case may well grant you your visa. But if caught on a lie you will get a ban because of that.
So yes, your one day overstay might lead to not getting a visa, but lying about that ban will lead to other bans if found out and that can be while applying for a visa or at the border, where you are interviewed. So better be upright about it and hope for the best.
Yes, your South African ban could harm your chances of getting a UK visa.
AFAIK African countries do not routinely share immigration data with European countries. However, when applying for a UK visa you are obligated to disclose all overstays and bans, no matter the reason, how long ago the overstay, or how long a ban was for. Deliberately not disclosing counts as deception, and would result in a lengthy ban if discovered.
Credit:stackoverflow.com‘
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