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I have only just found this website and so you probably have your answer but if not I hope this info helps you. I believe Walton park cemetry was a very small part of land which was owned by St Mary the virgin church (c of e)  Walton on the hill. - St Marys is a high church which has/had many smaller ones 'under' it. When the port of liverpool began to expand it became too far for sailors to travel to St Marys - they went into the pub next door (black horse) and then would be late back to the boat. To stop all these problems a church was built in Liverpool called St nicholas (both still standing) the ownership of the cemetry was transferred to St nicholas where I believe it still is.  If so the church would have records etc. The church of St Peter in Liverpool was demolished and all the graves (possibly thousands) transferred to Walton park cemetry,  these look like two fields which have sunken in places. A lot of graves have sunken over the years. Yes there are lots of paupers graves as walton hospital and workhouse backs onto the site. There are also soldiers graves, Robert Trussell etc. Hope this helps you with your research