Dear Kilkenny
I have only just seen your question today, but I still hope you see my response. Very nearly the exact same thing happened to my mother.
She gave birth to a stillborn baby girl in Romford in 1958 in my aunt's prefab. The midwife, nurse Sexton, said as it was my mum's first baby, it would be a while before her labour was in full flow, and went off to deliver a lady's third baby. By the time she got back, my mum was in trouble, and had a huge haemorage and lost a lot of blood and lost consciousness. When she came round (still at my aunts prefab), the flying squad was there with her doctor, and her baby was gone. She never even as much as saw or held her baby. Just like with your mum, there was no counselling, no funeral, nothing. They (the doctor/mid-wife/hosptial) treated it almost as though it had never happened.
When my mum first told me of this many years later (in the 1980's), I called Old Church Hosptial (I know it has gone now), and they checked their mortuary records and said my mum's baby had been taken to Co-op Funeral Directors in Rush Green (tel is 01708 752617), so I don't know if that was an arrangement the hospital had with them, but you may want to call them . They looked in their archive records and told me my mum's baby had been buried in Eastbrook End Cemetary, (tel 0208 270 4740). This counts as Dagenam and Havering Council, so if you had no luck with Romford Council, you may want to spread out the area you search a little and start with them.
I know others here have said babies were sometimes buried with an adult, and I know this could sometimes be the practice, but my mum's baby was buried in a plot with 15 other babies who died around that period, with each grave containing 4 babies, so not all cemetaries have the same practices. At last, after nearly 30 years of not knowing, my mum got to see the final resting place of her first little baby girl. We have a granite vase on her gra