This is St Leonards Church and is now linked with the Parish of St Ambrose (I have a cache there too if you haven't found it yet).
St Leonards church (or should we say churches) form a picturesque group, which can be appreciated better from the recently-formed green opposite in the winter months before leaves on the trees block the church from view.
Origins of the church go back to that of St Nicholas in the City, to which the parish of St Leonard City was joined on demolition of that church in 1771. The vestries of both churches were endowed with property, which in turn founded the mission area of Redfield which first met in a baker's loft in Blackswarth Road in 1906. This was not received well by the vicar at St George Parish Church which had to surrender parts of its parish (and thus his stipend!) for the new parish.
The foundation stone is preserved by the south door of the west narthex. It was laid on October 8th 1907 and records the name of the architect W.V.Gough. The church of St Peter and St Paul was completed the following year. It consists of a four-bayed nave with west bellcote and west narthex (having both north and south entrances), lower narrower chancel, and to the north large more domestic schoolrooms and vestries etc. This is now used as the church hall.
In 1925 in recognition of continued support from St Nicholas City (contributing towards the earlier Scout Hut and vicarage built that year), the dedication was changed to St Leonard from St Peter & St Paul.
The foundation stone for the new church was laid on 25th June 1938 and consecrated on November 5th in the same year. The architect was Robert Potter. It is still vaguely Gothic in style and feel, and of traditional plan. Nave and chancel in one, with a four-bayed north aisle. A passageway connects the old to the new, which has an open cloister walk and a small enclosed garden to the east.
(Thanks to ChurchCrawler for this information).