It does sound like you were mis-informed, and sadly that seems to be common with banks all over. The only account that is legally restricted that I can think o

It does sound like you were mis-informed, and sadly that seems to be common with banks all over. The only account that is legally restricted that I can think of is the ISA which offers good tax incentives for saving but with a limit to how much can be contributed in a year, and I think you can only open with one provider in a given tax year.