I have connected through LHR innumerable times without a single bad experience or missed connection. Yes, you have to be prepared for long walks. Yes, the lines for the FCC buses can sometimes be long. Yes, the lines to reclear security at your connecting terminal can sometimes be long. But somehow it all works out and you make your connection and you quickly forget about the hassle. Or you can stress about it and allow it to ruin your trip. Let your wife choose.