The witnesses may have worked with Emily. I can't see Bessie to pin her down.
Have we discounted this family, Merton is just up the road from Carshalton

1891 Merton - 4 Railway Houses RG12/603 f80 p58
George Budd 35 bn Headley, Hants - Railway plate layer
Louisa 29 bn Surbiton Hill, Surrey
William 4 bn Mitcham, Surrey
George 3 bn Merton, Surrey
1901 - 4 New Railway Cottages
RG12/656 f36 p26
Louisa Budd - Wid - 39 born Surbiton Hill
Henry G Budd 13
Annie Budd 1
Rosie Budd 8
Emily Budd 5John Alfred Budd 3
Children all born Merton