The 'Smile' hitmaker tied the knot with the 'Stranger Things' actor, 45, in Las Vegas earlier this month, where their nuptials were officiated by Elvis Presley impersonator Brendan Paul, who is the owner of the Graceland Wedding Chapel where the ceremony took place.
After the wedding, the 35-year-old singer headed back to London where she lives, and spent two weeks in quarantine as part of the UK's coronavirus guidelines.
However, it seems Lily doesn't want to spend too much time away from her new spouse, as it has now been reported she is set to ditch the UK for good in favour of moving to New York City to live with David.
Before she moves, she'll have to negotiate a custody agreement with her former husband Sam Cooper over their two daughters, Ethel, eight, and Marnie, seven.
Lily and Sam finalised their divorce in 2018 and currently share custody on a week-on, week-off basis, which will prove more difficult if she moves to the US.
A source told The Sun newspaper's Bizarre column: ''There's a lot to sort out, not least how she will co-parent. In the end one of them is going to miss out.''
Meanwhile, the 'Not Fair' singer recently said she fell for her husband when he wore her ''terrible merchandise'' on their first date.
David donned a T-shirt with her name on it that he bought on eBay and branded Lily's official merchandise as ''cr**** quality'', and the singer was endeared by his honesty.
She explained: ''Ever since the beginning of my career - I suppose it's my self-hatred and low self-esteem - I presume no one would want to have Lily Allen written on a T-shirt
''David wasn't impressed with my last merch. He said it was hit was cr**** quality and he got some off eBay.
''We were on our first date in London and I went round to his place he was like 'Do you think I should wear this or not?' It was terrible. It wasn't even Fruit of the Loom and it was green. I was like I am sure I have never approved that.''
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