Can't speak for Manch, but as eastern says, we generally can work out the wind fairly accurately given the difference between your airspeed and our groundspeed display, and your allocated radar heading and your displayed track. As long as the wind affects most planes in a similar way it's not too bad. As long as you remember which ones have to turn onto the ILS early.....!
When the crosswind is strong at altitude but drops away significantly at lower levels, one heading will obviously result in a long curved track. In that case you might have to take several 'nibbling' heading adjustments. We know you can fly a track instead...but then the CAA considers you to be on your own navigation and therefore not technically radar separated from adjacent traffic. Doubtless this will change one day but we're stuck with headings for the moment.