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Banking options for a non-resident UK Holding company

I am afraid that your chances are quite low, currently :(
UK companies with non-resident director(s) have real troubles with banking, nowadays. Brick-and-mortar banks are usually no-go. Have a look at Moneycorp Bank (I do not mean Moneycorp money transfers). As for EMIs, try perhaps Airwallex, Currenxie, Verifo ... or search here for some tips for UK EMIs...