Found he was Silver Badged Discharged on 14 June 1916 as Pte 33574 John Parry
I believe that you have attributed your SWB information to the wrong man.
John Thomas Parry (33574) enlisted on the 25th August 1914 into the Manchester Regiment. He gave his age as 38 years and 4 months. He declared that he was born in Duckenfield, Cheshire and that he worked as a collier. He was married (wife Ellen) and he resided at 19 Peel Street, Ashton under Lyne. He transferred into the 2 Liverpool Regiment on the 4th November 1915 and to the 3 Liverpool Regiment on the 29th April 1916. (please see image attached).
The John Parry that you are looking at (service number 8533) originally enlisted in May 1903 (service number 7943) giving an incorrect age. (see snip of image of attestation). You can see a notation in red ink 'joined

?? 27 July 1903'. I then looked for a SWB entry for a John Parry that gave an enlisted date of 1903, either May 1903 or July 1903. I found that a John Parry (9533) of the 3rd Battalion Liverpool Regiment, was medically discharged on the 10th May 1917. Please note his enlistment date, i.e. 27/7/03 (snip of image attached). I am sure that this is the man that you are looking at despite the slight difference in service numbers. (I can not find a Parry with the number 9533 in the Liverpool Regiment). I also attach his SWB card.
Still trying to find his MM entry in the London Gazette.