The Conservative Party launched an 'Equalities Manifesto' 3 May which makes a number of commitments on LGBT rights.
Under the section headed 'Fight for LGBT rights around the world' it says (my emphasis):
Unfortunately there are still far too many countries around the world that discriminate against gay and lesbian people. We would use our relationships with other countries to push for unequivocal support for gay rights. For example, shadow Cabinet Minister Nick Herbert will attend the EuroPride rally in Warsaw as part of our commitment to making the case for gay equality in Eastern Europe.
We would also use our influence in international groups like the Commonwealth to put pressure on countries where gay people are persecuted, such as Uganda, and we would change the rules so that gay people fleeing persecution were granted asylum. At the moment gay asylum seekers are often returned to countries with homophobic regimes and told to keep their sexuality a secret.
This means that of all the major parties only Labour has gone into the election making no commitments on LGBT asylum.