The churches of Eaton and Hulme Walfield belong to a group of parishes, known as a Benefice. All of them share the same vicar and curate. The group has a page on this website: https://www.achurchnearyou.com/church/12764/benefice/

The page on A Church Near You for St Michael's Church at Hulme Walfield is https://www.achurchnearyou.com/church/12767/ 

The other parishes are:

Swettenham, where the church is dedicated to St Peter
http://www.stpeterswettenham.org.uk

Marton, with the church of St James and St Paul
http://www.martonchurch.co.uk

Siddington with Capesthorne. Siddington's church is dedicated to All Saints. 
http://www.siddingtonchurch.co.uk/

Services are held occasionally (usually for Harvest, Christmas and Ascension) at Holy Trinity, the Chapel of Capesthorne Hall.