Same awful experience here.
When I arrived in the UK they looked like a solid bank due to their branding so I wanted to open my first account there. After several one-hour appointments and hard searches on my credit file (which ruined my credit 3 days after arriving in the country, thanks HSBC 
) they declined my application as the proof of employment (a printed PDF sent from the head office to my employer’s local branch) according to them didn’t have the proper letterhead. 
WTF does that even mean - every company has their own design guidelines that define what the “proper” letterhead is. If it’s about money laundering they shouldn’t be looking at the letterhead in the first place - call the company directly and ask them to authenticate the document, as a fraudster will easily forge any letterhead they so desire.
In the end I went with Nationwide - still legacy rust but at the very least they opened the account with no issues. One thing is certain though, I am never going back to a legacy rust-based bank again. I’d rather deal with the shortcomings of challenger banks (like the lack of Apple Pay) than go through this nonsense.