Maybe I can offer some help there, but not an elegant solution. I noticed that looking at the storage on my device that the UA app was taking up almost 1GB and saw that I had 615MB of user data plus the app itself, which is ~220MB, so I clicked "clear storage" (Android) and after logging back in my user data is now 1.5MB. And I haven't taken a flight or booked one for coming up to a year now. It all looks as it did before I cleared the storage.
But, it does mean all the recent searches have gone.
Quite what was in that 615MB I have no clue. Seems an awful lot to me for an app that is not used at the moment and hasn't been for almost a year.