It doesn't matter which name you use - the name on your visa matches the name on your passport, right? As long as the name on your passport matches the name on your airline ticket, you'll be fine.
You can book tickets using your married name and continue to travel on a passport with your maiden name - just make sure to bring along a copy of your marriage certificate in case there's any trouble with identification. It's one more thing to keep track of when you travel, though, and so if I were you, I'd just keep things simple and book your tickets using the name on your current passport. You can always send off for a new one just before applying for ILR, so that the names will match up again!