No, one of the UK government's is exactly that people will have a different sex either side of the border; it's in the statement I linked to at post #8:
"The Bill does not purport to require that a Scottish GRC issued under its terms would have any legal effect other than in Scots law; it could not, within legislative competence, have done so. It is highly problematic both in principle and practically for a citizen of the UK to have a different gender, and legal sex (including for the purposes of the 2010 Act), depending upon where they happen to be within the UK, and which system of law applies to them. It is practically and legally undesirable for all, including in particular the individual holder of the GRC, that a person will have one legal sex in Scotland and a different one in England, Wales and Northern Ireland."