His birth certificate will give you the details you require (or at least it will give his mother's name). You can order it direct from www.gro.gov.uk for £9.25 including postage using this reference:

Births Dec 1892
Fearn Wilfred Bakewell 7b 765

The reason why I think you may not find a father's name on the certificate is that there is no married FEARN couple of child bearing age in Starkholmes around the right time. There is a FEARN family in 1891 headed by Hugh and Mary A who were in their late fifties. The 1891 census shows an unmarried daughter Florence, aged 28, and two other children Robert (10) and Beatrice (4) who, if you look closely at the image (RG12/2776 Folio 84) are enumerated underneath Florence as "" son and "" daughter, suggesting that they were indeed her children.