You have decent options in Isle of Man, Channel Islands, and Gibraltar: Barclays, Lloyds, RBS, and Standard Bank. They usually want 25 ”“ 50,000 GBP to open an international account.
Otherwise, off the top of my head (and assuming we're avoiding garbage banks strewn across the Caribbean and South Pacific)...
Handelsbank and Privatbank1891 in Germany.
SEB or Nordea in Sweden or Luxembourg.
ABN Amro in Netherlands.
Bank Frick in Liechtenstein. You can try other private banks in Liechtenstein and Switzerland. 100,000 GBP is on the lowest end of what they would accept (usually it's 250-500,000 CHF minimum).
ING in Luxembourg and maybe Belgium. With Brexit, this bank has become more difficult.
Signature Bank in New York but you might need an introducer.
Swissquote in Switzerland, but they aren't suitable for third-party transfers (only to/from yourself).
Butterfield Bank might be an option.
Expect thorough, in-depth KYC. That's just the reality of banking nowadays. They either ask you upfront or they come asking a few months later anyway ”” or both.
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This is the probably the answer to your question.