Unfortunately, west bound from the UK doesn't give you a choice of many decent economy class options. Going east its a different story with all of Skytrax 5* airlines such as Singapore/Qatar/Cathay/Asiana/EVA/ANA/Garuda and Hainan available and a good selection of 4* such as Emirates and Turkish.
Note that there are only two US airlines that make the 4* list, JetBlue and Virgin America most are in the 3* category along with the likes of Air India and Egypt Air. Spirit are 2* alongside Iran Air and Turkmenistan Airlines.