The Arctic Monkeys frontman penned the heartfelt track, 'Fire And Thud' - for the band's new album 'Humbug' - in which he sings about the pain of discovering the British TV presenter was moving to New York.

The lyrics include: "If it's true you're gonna run away/Tell me where, I'll meet you there."

Although his band is based in the UK, Alex - who has been dating the British beauty since July 2007 - decided to move to New York with Alexa and the couple recently bought an apartment in Brooklyn.

A source said: "Alex is really excited about the new place. It's the biggest investment he's ever made and he wants to make sure he spends as much time there as possible.

"Any spare second he gets off he is trying to spend in New York with Alexa."

Alexa - who hosts her own MTV show 'It's On with Alexa Chung' - recently revealed she in awe she is of her 23-year-old boyfriend's songwriting skills.

The 25-year-old former model said: "Alex is so wise, it's ridiculous. I don't know where it comes from. Especially when he hasn't even experienced some of the situations he writes about."

'Humbug', the Arctic Monkeys' third studio album, is released in the UK later this month.