The HCT-900 and Hakko FR801 are the cheapest name brand hot air stations I'm aware of (350GBP before VAT & shipping). Cheaper than that, you're looking at used, or a much cheaper Chinese model. If it matters to you, the HCT-900 is also made in China, and the Hakko is still made in Japan.
JBC makes two sizes of hot air station, the smaller one meant for things like cell phone rework/repair. That one would be suited IMHO, but it's definitely not cheap.
FWIW, tweezers are really handy to both position and keep it from blowing away. When you feel the part drop, let go and move the heat off simultaneously. Surface tension will do the rest. Takes a bit of practice, but it doesn't go flying across the board.
But I like georges80's suggestion of using a hot plate, and think it would be more cost effective than a new, name brand hot air station.