I think we need to write to Debretts (David Williamson is now dead) to ask if they actually had sight of the Letters Patent otherwise I would find it hard to accept their assertion. It would effectively mean that his eldest daughter had a fundamental right to call herself and be referred to in all legal documents as Baroness or Lady Home of Berwick. But in fact there is not one document - notably her Testament - that I can find that refers to them as such. Merely as his daughters with the honorific 'Lady' because they were daughters of an Earl. In addition, Debretts cannot settle these issues. Did Alec Douglas-Home make a claim in The House for that Peerage to be added to his stable? Because that seems to be what they're saying. Frankly I would treat such a suggestion with disbelief.