According to Dr Ben Felderhof in "The Shire Way" it was previously Woodside Cottage at 430 Lickey Road (see point 2 of the Executive Summary) Here's a (poor copy of) the map.
And an extract about Woodside in italics. John Till was the retired postman and his cottage was beside the entrance to the Oratory Retreat.
By the summer of 1904, Mabel had recovered enough to be discharged from hospital, although she may have been advised that she would benefit from a spell in the countryside rather than returning to cramped accommodation in the city.317 Father Francis Morgan proposed that she convalesce in Rednal, a small village eight miles south-west of Birmingham, where Cardinal Newman had built a house which the clergymen of the Oratory used as a ‘Retreat’ [Map 8:A]318.He found lodgings for her and the boys in ‘Woodside Cottage’ (now Fern Cottage) [Map 8:2],beside the entrance to the Retreat. The cottage was owned by a retired local postman, John Till (1849-1923), and with Mabel in no state to cook, the Tolkiens would have their meals prepared for them by John’s wife, Louisa Till (1849-1928).319 And so, in June 1904, Mabel met her two boys on a train, describing their appearance as that of ‘weak white ghosts’, and together they travelled to their new home.