I would suggest that the above Mary Kate Clarke, being RC, and if she died in Widnes, would have been buried in St Bede’s RC churchyard in Appleton (a part of Widnes). She could not have been buried in Widnes Cemetery as this did not open until 1898.
The records for St Bede’s churchyard have been transcribed but are not online. The transcription is held by the Widnes Group of Liverpool & South West Lancashire FHS.
If her family were living in Gerard Street at the time of her death it is probable that the funeral service was held at St Marie’s RC church before burial at St Bede’s churchyard (St Marie’s did not have its own burial ground). The burials from St Marie’s have been microfilmed and the records show the place of burial, if it was at St Bede’s this is invariably described as “Appleton”. This microfilm is available at Lancashire Records Office and Widnes Library.
(Note that there was another street in Widnes with a similar name, Gerrard Street. This one was located in the Simms Cross area and was roughly the same distance from both St Marie’s and St Bede’s, so if her family lived there the funeral service might have been at either church. The other street, Gerard Street, was in the West Bank area, and therefore closest to St Marie’s.)
