I think I'm in the right spot, if not please feel free to redirect me 
Daughter and partner are early-mid-twenties, good credit histories, secure jobs, and a 10% deposit, but they can't make any sense out of what they're able to get mortgage-wise. One back changed its mind halfway through the process (willing to lend a heck more than the online thing did but then wanted 15% deposit), one won't say until they have a property in mind (which they can't do till they know what mortgage they can get...). It seems like a heck of a runaround for people who are a pretty secure bet.
So wise vipers, how does one go about getting a sensible and reliable mortgage offer these days?