"It is with a heavy heart that we are going to need to cancel our upcoming shows at Latitude and Bournemouth Academy," the indie rock band said in a statement.
"Alex collapsed at Seattle airport on the way to London and has been hospitalized with a chronic stomach complaint," the statement continues. "We are devastated to have to cancel shows that we were so looking forward to. We can only apologize and hope for your understanding at this time. Love TDCC x."
Festival organizers announced Allen's new gig on the Obelisk Stage Friday. The British singer said in a statement she was "so sorry to hear about" the incident, adding she was "more than happy to step in."
"I've never been to Latitude but I hear it's fabulous and I can't wait to get my heels on for some serious dancing action on Friday evening -- so, so excited," she said.
The festival, which has been held annually at Henham Park in Suffolk since 2006, attracts around 35,000 attendees each year.
2014: The Year in Fashion [PHOTOS]
S Club 7 to reunite for BBC charity event