One of the party favourites here, this topic, apologies in advance for some comments which may ensue downthread! Here is my favourite previous thread on the topic, there may be a few others too:
http://www.flyertalk.com/forum/briti...ess-class.html
You don't have to pay. You get free seat selection at Online Check In stage, and starting from AMS you have a few hours' advantage over those starting from London since online check in will open a bit earlier for you.
But yes, unless you have a corporate deal or status on
oneworld then you do have to pay for seat selection. Some here hate it, some here love it (I do!), and there won't be much meeting of minds, until you get a shiny card or two, I guess.
If you fly more than a few times a year, get yourself at least a BA Bronze card, or another
oneworld Ruby level card, it's mainly occasional leisure travellers who get hit by this. Or wait until OLCI.