Some lenders do, some don't and pop you on the variable rate. Hopefully they take the enlightened view and base their decision on past performance, rather than a credit check. After all, they still have the same security.
My opinions are merely that .. opinions based on experience. Always seek professional advice.
IVA Completed 23rd July 2013 .... C.C. 10th January 2014 http://foggy.blogs.iva.co.uk