In fact BA are probably one of the better airlines if you want to get some landings in. Ive been flying with them for about seven months now and a quick check of my log book shows that I have done more than 50% of the landings. Things like X wind limits dont really come into it much, as on the pre flight you decide with the skipper who will do which sector and if the wind is out of limits at the destination, you simply do the return leg. In 350 sectors (180 as picus) i have left control with the skipper once as a result of a wind check update.
Most skippers are more than happy for you to do visuals as well.
Dont chuck that form in the bin just yet (and remember that it wasnt that long ago that certain charter co's insisted that the FO requested that the skipper gave him a bit of speedbrake rather than just using it himself)