To answer your question regarding depth, most professional cake makers like myself make our tiers approx 4 inches in depth which is 10cm.
I think Waitrose are the same as M&S - WR used to do a chocolate cake decorated with white chocolate cigarillos (they may still do it - I have no idea). The commercially bought cigarillos are 4 inches (10cm) in depth and I make my chocolate cakes the same depth as the cigarillos, their stacked cake effectively has one cake sitting inside the other as the cigarillos are much taller than the cake.
The pic above with the couple cutting their cake shows the cake displayed on a standard size silver cake stand, I have one in the same design as do lots of venues that I deliver to. There is roughly a 1.5 inch ring around the stand where the base cake board is smaller than the stand. The bottom tier of a professional cake, standard size/standard cake boards, would fit the top of that stand.
These are the facts, I can't advise you what to do because obviously I'm biased - depends if the depth/size of your cake is important to you.
Catherine