Looking at
https://www.railmaponline.com/UKIEMap.php (stations are not shown by default but can be turned on).
There was never a railway at Newtown Linford. The nearest was a branch finishing about a mile to the south with no station, probably serving a local colliery.
The nearest station would have been Glenfield, on a route that entered Leicester from the west and terminated there, which would therefore never have had a service to Nottingham. According to Wikipedia this replaced an earlier station in 1875 and closed in 1928.
The nearest station with a service to Nottingham would have been Belgrave and Birstall about 4.2 miles away on the Great Central main line, opening in 1899 and the station closing in 1963.
http://www.disused-stations.org.uk/b/belgrave_and_birstall/index.shtml has details and a sample timetable though only from 1950. I have not quoted text from this site because none of it is relevant to the topic.
Leicester Central station on the same line was only a bit further and had a better service as the fast trains would have called there too.