Hi slowlysinking,
I have only last month changed my bank via the switching system. It didn't prompt a re-assessment, however, I was required to go visit my local jobcentre with 2 forms of ID, my old bank and new bank details. This is just to clarify that they've got the correct information. I used my Passport, Driving License, but also took my C/Tax bill, so they had proof of my address. It took a matter of minutes. I didn't have to book an appt, I was told just to come down at my convenience, and they'd fit me in. I did however had to get someone to come with me, due to my anxiety around people, and panicking thinking it would be packed, but it wasn't.
Regards, Chris.
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