Bogey -
I would go with Plan B, get your golf in once your wife is on her way home. Getting to (and then finding) the golf clubs in the suburbs of London is not easy and can take some time. If you have all day to avail yourself of the various 36-hole clubs (Berkshire, Sunningdale, Walton Heath, Wenworth, etc.), your time spent traveling about will be much more productive. In fact, once you have finished sight-seeing in London, you might want to find a nice B&B/hotel somewhere in Surrey and base yourself there for the 2-3 days you will be playing golf in that area.
DT