Yes, of course – timber frame is the most widely used method of construction, accounting for over 70% of all new builds in the developed world. You will have no difficulty whatsoever getting a mortgage for a timber frame house versus any other method.
As Patrick Sawdon, former Head of Halifax Valuation and Surveying, pointed out; “Timber frame housing is equally as good as housing constructed from brick or block. We make no differentiation on the lending terms offered on either form of construction.”
Similarly, Steve Birt of Zurich has said that “Insurance companies draw no distinction between modern timber frame and brick or block construction.”