PICTURE EXCLUSIVE: Ready to face the music? Madonna finally arrives in London as she plans to 'get estranged son Rocco Ritchie back in school'

Madonna returned to the UK on Thursday morning for the first time since her son Rocco Ritchie left the Rebel Heart world tour to live with his British father Guy Ritchie.

The musician looked like she was meant business as she arrived at London's Heathrow Airport from New York's JFK after entering into a bitter custody battle with her ex-husband over the 15-year-old.

The 57-year-old mother-of-four reportedly made plans to come back so that she could get Rocco back in school following his term-time Maldives holiday with Guy, 47, and his new wife Jacqui, 34.

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Guess who's back: Madonna returned to London from New York on Thursday, no doubt ready to face son Rocco Ritchie who is embroiled in a custody battle

Her outfit didn't seem to reflect a bright mood, since she was top-to-toe in black and hiding behind her tinted sunglasses as she walked through departures.

Madonna wore a polka dot jumpsuit and masculine shoes but the main feature of her ensemble was a strange coat that was completed with the measurements of each design detail, including the width of her lapels and the length of her sleeve. 

She has just completed 82 global concerts that earned over £120m and reached over a million fans around the world. 

Game face: The blonde wore dark shades as she made a high profile arrival in London

Ready to face the music? The musician, here at New York's JFK airport, has not been back in the UK since her son abandoned her on tour

She means business: The star reportedly plans to get her son back in school following his term-time break

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She's on her way back to the UK and for the long flight Madonna looked comfortably dressed.

The superstar of course didn't let her comfort get in the way of her style though, choosing to don a cool polka dot jumpsuit for the flight teamed with unusual outerwear.

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Home at last: When the queen of pop arrived home, there were plenty of friends on hand to help with the bags

But the musician, who is a mother to two biological children and two adopted children in total, made time for some shopping in Uptown New York with her daughter Mercy James before leaving the city, on Tuesday.

Madonna has now hopped straight on a plane because it's thought she has hopes of being reunited with her eldest son in order to repair their relationship. 

She will have just missed the family though unfortunately, since Jacqui and Guy are currently holidaying in the Maldives with all of the children. 

Estranged: Rocco has been living with his father Guy Ritchie and his stepmum Jacqui in London, ever since quitting the world tour

Holiday makers: Madonna is said to be worried for Rocco's education after Jacqui and Guy took him on a term-time holiday to the Maldives

Happy families: Madonna's eldest son is said to have joined the couple's three young children on the break

It is no doubt a welcome break from the ongoing custody battle, in which Madonna has already won the right for the hearing to be conducted in New York rather than London.

A source told The Sun newspaper last Monday that Rocco's mother is concerned for his education since newly-married couple Jacqui and Guy decided to take him out of school to go on their holiday.

The insider said: 'She has said she is prepared to fly over to London when Rocco gets back and take him to school herself.'  

Bag ladies: She certainly seemed to have packed plenty of luggage

Moving about: She has been all over the world with her Rebel Heart tour

Finally home: The star was back in London after a very long stretch

Still smiling: Madonna revealed a wide and satisfied smile as she touched down

Many hands: She was helped through the airport with her luggage while fans took pictures

Just one bag: But she carried only her Gucci handbag while the other luggage followed

Dressed up: It was quite an outfit that she had pulled together, complete with gloves

Courting attention: Even though she was in black, she couldn't be missed with her high profile arrival

They continued: 'Madonna is concerned Rocco is going to be missing so much school. She wants Rocco to relax but his education is very important.' 

Rocco has been living in London with filmmaker Guy and his new wife Jacqui, along with their three young children, ever since reportedly abandoning his mother before Christmas. 

The teenager is said to have walked out on the global tour when she took away his phone because she wanted him to focus on his studies, The Mirror reported in January.

A London welcome: She was welcomed into the UK with suitably grey and wet weather

Who's that girl? The star has just completed an 82-date tour, but she was looking well

Looking well: The blonde was flying by herself it seemed, without her children

Rocco is alleged to prefer his 'normal family life' in the British capital with his filmmaker Guy, stepmum Jacqui and their children, spending weekends at Guy's Grade II listed Ashcombe House in Wiltshire.

Madonna and Guy later entered into a custody battle with hopes of coming to an amicable agreement over their son. 

Meanwhile this week, Madonna has been entertaining her 6.6M followers with pictures of her eldest daughter Lourdes Leon. 

Throwback: Madonna, meanwhile, has been entertaining 6.6M followers with pictures of her eldest daughter Lourdes

Good things are coming: Madonna shared a picture that was captionned 'good things are coming' this week

Happy families: Madonna is mother to Lourdes (left here in a throwback shot), David Banda (centre) and Rocco (right) as well as Mercy James

Lourdes, 19, is Madonna's daughter from her fleeting relationship with Carlos Leon in 1994, while her younger daughter Mercy was adopted by the musician in 2009.

Madonna and Guy share a second son, David Banda, the former Malawi orphan that they currently share joint custody of after welcoming into the family in 2006.

Formerly married to actor Sean Penn for four years, Madonna wed Guy in 2000 and they spent eight years together before divorcing. 

Guy married his second wife Jacqui last summer and they now have three young children Rafael, Levi and Rivka.

Quality time: She made time to take daughter Mercy James shopping in Uptown NYC on Tuesday

New season: She's said to have picked up the new season Gucci bag before it's even hit the shops