Does anyone know if you have to apply for a visa waiver programme from UK to travel through American airspace? My travel agent hasn't said anything but a friend who is going on a caribbean cruise has been told she needs this and may be refused entry. Any help appreciated.
The simple answer is no. But if you are to, say land and pass to a port then you are entering the US, i.e. going through US passport control (immigration) and for that you need to be entitled to enter - for most people that means a visa.
You do not say if you actually land in the USA - if you don't then you do not need the ESTA - but you may as well do it anyway, it takes about 2 minutes and it is currently FREE.
It is better to have it just in case your plane goes tech and you have to land in the USA, then you are covered.
Here is the FREE ESTA link: https://esta.cbp.dhs.gov/esta/esta.html
If you are going on a cruise then this is the best site in the whole world :http://boards.cruisecritic.com/index.php The 'ports of call' section is especially useful. Please give this link to your friend too.