I had the same problem with HSBC.
In fact, I've had many problems with HSBC, ranging from the customer services who opened my account for me (and didn't give me any information on the account) to the fact that they told me, when I applied to increase my transfer limit from 0, that my signature was not the same as the one used to open my account, to declining me a credit card without explaining why.
For starters- my signature has been the same since I was a teenager. It will not always be an exact replica. If they are going to be so a**y about it, they should really hire a handwriting expert or something along those lines.
I emailed them online via my bank account portal asking them about the status of my application. So, it must be the same signature coming from the same person (unless I was very unfortunate).
They still kept insisting that they could not increase my credit limits and each and every time told me to go back to the branch I opened my account with and review my signature on my form there...and...each and every time they said I had forgotten my signature.
A bit of persistance and they processed my original transfer form, but still had the cheek (and this is bad customer service- insulting your customers) to tell me that I should still go back to look at my signature as I have forgotten it.
My credit card got declined for no reason. I asked why; turns out they did not have "proof of my salary" (when I opened my bank account they had a copy of my employment contract). I then pointed out (about 10 times) that their online application form did not ask for a copy of my salary statements/contract to be sent and merely asked for a copy of my ID. I therefore stated that they should not have immediately declined my application if they felt they were missing something in order to process it and instead they should have asked for my salary statements etc if they required them first.
Eventually they processed my application "in the light of everything I had mentioned" (I never sent them proof of my salary and at this point did not have 3 months salary paid into my HK account) and gave me possibly the largest credit allowance I have had, ever. Hmmm. I only want to use it to pay for my holidays which I will pay off immediately; I don't like credit.
HSBC UK I have never had a problem with.
If SC is miles better, I will think about moving to them soon.