Hi Rosie
Cecil T Butler aged 3 and born Leicester is on the 1901 census in Leicester RG13 3007 folio 163, son of Frederick William Butler and Emily nee Cole (married Pembroke 1886).
It really is always better to go from the known information. Otherwise we have a tendency to grasp at coincidences which have a habit of causing us to shoe horn the information into 'the fit we want'
Cecil Talbot Butler born Leicester 1898 for Frederick Talbot born 1899 Kentish Town.
It also requires the more complex hypothesis of illegitimacy in Leicestershire, the taking of the child away from his natural mother (while Walter lurks suspiciously back in Leicestershire) and the acceptance by Walter's wife of her husband's son with another woman.
It is a more complex explanation than a simple fostering of a child through the London poor law system or a private arrangement, which allows the family to become attached and ultimately informally to 'adopt'.
Simple explanations should be persued first and eliminated before turning to the more complex.
I know that isn't necesarily the easy answer, because obviously the Butlers as genetic parents would be a lot simpler to research, but Fred Talbot could still be a child from the Butler's extended family. Regardless of whether he is or isn't, you will have to research him to either try to prove he is Frederick Butler, or to eliminate him. He is at present the only known candidate you have.
The internet is wonderful but it does work against us as well, by having some records instantly available but many others only available through hard work in record offices. Consequently we keep coming back to what we can easily access because we very much want the answer to the puzzle and we want it now.
I'm afraid my last advice which was to work from the known information from the 1901 census hasn't changed.
It might be worth checking through Lambeth and Pancras poor law records to see if you can find the child entering the poor law system (workhouse, children's home) and exiting to the Butler family.
It isn't easy and it might ultimately be fruitless but unless any further information is known or becomes available, perhaps through descendents of the other Butler children, it is a logical set of records that could be searched.
Regards
Valda