The 'Smile' singer and husband Sam Cooper welcomed their second child Marnie Rose Cooper on January 8.
The performer took to Twitter to express her alarm at her poor postnatal treatment.
Allen told her 3,950,604 followers that she contacted medical officers of the NHS after being discharged from the hospital, and later set up a home appointment for a check-up on her newborn.
She tweeted at NHS Direct: "Hi there, can't seem to find out which hospital's community midwifery team are coming to see me… I'm starting to worry now, and no one answers the phone, or if they do, I just keep getting passed around. Let me know if you can [help]."
The 27-year-old later added: "So after speaking to the Brent midwifery team at 7 this morning, I was told to stay in all day and someone would be over to weigh my baby and do a jaundice assessment as I've been a bit worried.
"Waited all day, and nothing, not even a phone call. She'll be a week old tomorrow."
Allen said that she didn't "mean to moan" about the situation, but was concerned about how "mothers with less support, both financially and emotionally are meant to cope... surely we can do better than this".
Turning her attention to the actions of the current government, she noted: "It may be worth mentioning that when I was discharged from hospital with my last baby,14 months ago the midwives were there 3 hours later.... #waytogocoalition #CUTS #nhs"
Allen later updated her followers on Tuesday afternoon (January 15), saying: "The midwife came this morning and everything is fine. Thank you everybody."
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