I work for a mortgage lender and I process these all day, every day.
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'Remortgaging' is usually when you change lender. If you're staying with the same lender, but moving to a different product after your fixed rate ends, they usually call it something like 'transfer of product' or 'switching package'.
In my bank, if all you're doing is moving from one fixed rate which is ending, to another fixed rate or other product in our range, and not borrowing additional funds, we don't ask for proof of income, and there's no need for a new valuation. You might have to pay an arrangement fee to get the lowest rate. Or if you take a slightly higher rate, the fee would be waived.
It's pretty easy and painless.
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