It is certainly possible to transfer your previous year's cash ISA allowances to an alternative bank or building society. This will not be seen as opening a second ISA in the same tax year as you are simply transferring previous year's allowances. However, as you have found, not all providers allow transfers in so make sure you check the small print before applying. Your existing cash ISA provider, Nationwide, are permitted 30 days to process the transfer to the new provider as soon as they receive the paperwork.
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