Just had a quick scan through Trip Adviser, 1 report referred to self service breakfast and another that both continental and cooked were available.
Both had been written in the last couple of months.https://www.tripadvisor.co.uk/Hotel_Review-g186338-d193098-Reviews-Thistle_City_Barbican-London_England.html
sorry, I haven't, and there doesn't seem to be a menu online; but the phone number is 0871 376 9004 if you want to call them and ask. Looks like it's in the 120 Central Brasserie, open from 6.30am.