A Gender Recognition Certificate automatically leads to a new birth certificate in the acquired gender and allows greater legal recognition, such as the right to marry.
Whether or not you have a GRC or even wish to apply for one it is not acceptable for someone to ask you for a GRC as a means of ‘proving’ who you are. It is also not necessary for you to have a GRC in order to be protected from discrimination under the Equality Act. For example, you should not be asked to produce a GRC to access facilities or services. If you feel un-comfortable about being asked questions about your gender identity or feel its being challenged then something is wrong.