A useful starting point here would be the article by Su Coates, 'Manchester's German Gentlemen: Immigrant Institutions in a Provincial City 1840-1920' (Manchester Region History Review, vol. 5, no. 2, 1991-92 - pdf file). Among the sources this refers to are the 'Annual Reports of the German Evangelical Church and School in Manchester', which are held by Manchester Archives and Local Studies for the years 1855, 1856, 1860, 1867-72 and 1875. Coates's article also alludes to the 'indeterminate origins' of the pamphlet by Curt Friese, 'Some thoughts on the history of the Germans and their church communities in Manchester, especially in the 19th century'. In the later 20th century, the main German Lutheran Church moved out of the city of Manchester to Park Road in Stretford.
From 1859 to its closure in 1911, the Schiller Anstalt was central to the communal activities of Germans in Manchester, and the Local Studies information index has a number of references. One of the members of the Schiller Anstalt was Friedrich Engels, who had earlier produced 'The Condition of the Working Class in England' based on his experiences in the Manchester area, while employed as an agent in his father's Manchester factory. There is a wealth of literature about Engels, including his collaboration with Karl Marx.
Coates's article also refers to the Society for the Relief of Really Deserving Distressed Foreigners, founded in 1847. She states that this was mainly supported by, and gave aid to Germans, who were in any case the largest immigrant nationality at the time. The original minutes and reports for the Society, covering the period 1847-1927, can be seen in the Greater Manchester County Record Office (GB127.M294/2).
Some background to the German community in Manchester is given in an article by Panikos Panayi, 'The Lancashire Anti-German Riots of May 1915', (Manchester Regional History Review, vol. 2, no. 2, 1988-89 - pdf file).
Manchester Archives Flickr photostream
The photographs above can also be viewed directly on the Flickr site where you will find many more sets on Manchester Archives Flickr photostream.