Way to find out a child's parents without ordering a birth certificate?

[jonw65]

Or could it be granny with her age completely wrong?
Died soon after the census.
GATTY, MARTHA       
Age at Death (in years): 64 
GRO Reference: 1891  J Quarter in CAMBERWELL  Volume 01D  Page 586

Buried 1 June in Southwark.

A possibility for Frederick's mum might be Alice Gatty from the family discussed.
Birth reg
GATTY, ALICE       
Mother's Maiden Surname: RUMSEY 
GRO Reference: 1866  M Quarter in CAMBERWELL  Volume 01D  Page 567

In 1881 she is 16, a servant in Camberwell
https://www.familysearch.org/ark:/61903/1:1:Q277-SWWB

Possible Rootschat exclusive! Since nobody seems to know much about Alice.
In 1891 she is Alice York, 26, born Camberwell
Husband here is Edmund York, a waiter
Living 18 Boyson Road, Newington
https://www.familysearch.org/ark:/61903/1:1:QMRP-T2M

Daughter born soon after
YORK, ALICE  FRANCES     
Mother's Maiden Surname: GATTY 
GRO Reference: 1891  S Quarter in ST SAVIOUR LONDON  Volume 01D  Page 128

Baptism at St George Camberwell, 10 July 1891
Alice Frances
parents James Edward + Alice York
18 Boyson Rd
Father a Waiter

Couple more
YORK, JAMES  EDMUND     
Mother's Maiden Surname: GATTY 
GRO Reference: 1894  M Quarter in LAMBETH  Volume 01D  Page 490

YORK, FREDERICK  THOMAS     
Mother's Maiden Surname: GATTY 
GRO Reference: 1895  D Quarter in LAMBETH  Volume 01D  Page 450

Double baptism later at Emmanuel, Camberwell, 6 Nov 1902
James Edmund, born 8 January 1893 (they forgot the year!)
Frederick Thomas, born 12 October 1895
Parents James Edmund + Alice York
Father a Waiter

In the 1901 census Alice has a new partner, Harry Warner, a carman, who she did not marry until 1913
Living in Lambeth. Another son, Ernest Warner, 1.
Alice Warner, 35, born Camberwell.
https://www.familysearch.org/ark:/61903/1:1:X9ZF-R98

WARNER, ERNEST       
Mother's Maiden Surname: GATTY 
GRO Reference: 1900  J Quarter in LAMBETH  Volume 01D  Page 351

The marriage
1 March 1913, St Mary Lambeth
Henry Warner, 67, Widower, Carman
+
Alice York, 46, Widow, father George Gatty, Labourer
(Father's surname transcribed as Gatts on ancestry)

I haven't found a marriage for Alice Gatty to Mr. York.

[jonw65]

I do think I'll have to order a certificate.

Yes, do. Be sure to let us know when you get it.