Here's how a typical discussion unrolls:
Bank: "To do X or Y, we require you to visit us in person or provide a written statement".
Me: "Here's my statement with a digital signature, attached as a PDF."
Bank (ignoring the PDF): "To do X or Y, we require you to visit us in person or provide a written statement".
Me: "The law says (specific citation goes here) that I have just provided a written and signed statement. Here it is again."
Bank (ignoring the PDF): "To do X or Y, we require you to visit us in person or provide a written statement".
By the way, I had this kind of stupid back-and-forth with mBank, which tries to position itself as a "modern and innovative" bank.
The only next step is to sue, but who would bother.
When I was sworn in as an attorney, they had us sign a book in the courthouse as part of the ceremony. They said that sometimes people used a fancy signature since it was a special occasion, and explicitly told us not to do that since they would sometimes be asked to compare a purported signature to one in the book.
A letter from the UK to Australia costs £1.35, or £1.20 for "economy".