The death certificate for Elizabeth Simpson wouldn't show her parents names. It'd likely show the name of her husband and his occupation, so you could at least be sure you have the right one but you wouldn't glean much more more information than we have already, if any.
Obviously we know her father's name and occupation from the marriage record and the 1861 census.
Elizabeth's burial record (I don't think anyone's posted this yet but I could be mistaken):
name: Elizabeth Simpson
buried: 04 Mar 1861; St James, St Pancras
age: 46 years
abode: 19 Holford Square, Pentonville
It's probably going to take quite a bit of time and effort to try and trace the various possible Thomas and Elizabeth couples, cross checking various records (baptisms, births, deaths, burials, censuses, marriages (in case of re-marriages)). I've had a look myself but haven't been able to positively trace any of them.
It's probably best if you can access the LMA (London Metropolitan Archives) records available on ancestry.com as you'll get more detail from the actual parish registers than you will from transcriptions. Ancestry do frequently have free access weekends that you can keep an eye out for, often during holiday periods. Or your local library may have free access.