Richards failed to make Roy Hodgson's initial 23-man squad for the tournament in Poland and Ukraine and then asked not to be selected for the stand-by list.
But the Team GB defender said: "I have always said I wanted to play for England,' said Richards, who will be in the centre of Team GB's defence when they face South Korea in Cardiff.
"Whether I get picked for the next game, it's not down to me. All I can do is keep knocking on the door.
"I will never turn my back on England. A lot of people asked me why I didn't go on standby (for Euros). It was nothing to do with not wanting to play for England.
"I wanted to play (get on pitch, not just be on standby). Stuart (Pearce) has given me the chance to play. It was a nice moment for me to be captain (when Craig Bellamy went off)."