Turkey began EU membership talks in 2005, but progress has been slow over disagreements on divided Cyprus and opposition from some European countries.
Baird said: "It is obviously a difficult time. But the message is that we just have to stay resilient, we just have to keep going.''
On Tuesday evening, the queen will attend a banquet hosted by Abdullah Gul, Turkey’s president.
Gul is a member of the ruling AK party, which is an Islamic-rooted organisation.
His wife, Hayrunnisa, is likely to wear a headscarf at the banquet, despite a ban on them in public and governmental buildings.
The Queen will also visit Istanbul and the western city of Bursa where she will attend a traditional Ottoman shadow puppet show, a fashion show and visit a mosque to listen to Quranic recitals.