RootsChat.Com

To avoid duplicating any research on this family (though I don't think there are any specifically about Elizabeth) - there are a number of threads on RootsChat about the family eg:
https://www.rootschat.com/forum/index.php?topic=875522.0
https://www.rootschat.com/forum/index.php?topic=682194.0
https://www.rootschat.com/forum/index.php?topic=676644.0

Park Lane shows on this 1906 map, between the Park Lane Brick Works and Park Lane Farm and Park Lane Collieries (running north/south).
https://maps.nls.uk/geo/explore/side-by-side/#zoom=17.0&lat=53.50838&lon=-2.65243&layers=168&right=ESRIWorld

Hello dmooney and welcome to RootsChat.

Unfortunately CalumD has not been online here since 2020, but hopefully he still has the same email address and will receive notification of your post. I'm sure he will be happy ot hear from you.

Perhaps you mean 1782? I can see the baptism of William BUCKLEY at Siddington on 31 March 1782, mother Elizabeth ("Eliz." on the image).
https://www.familysearch.org/ark:/61903/1:1:F3NJ-YPP

Modified to add:
familysearch have the Bishop's Transcript too:
https://www.familysearch.org/ark:/61903/1:1:NHHT-TYQ

I can't make out what comes after "March 31 Willm Son of Eliza Buckley Siddington ..." 

There are at least 16 William BUCKLEYs who came to Australia as convicts (on https://convictrecords.com.au). Just wondering how you know you have the correct baptism?

Also of possible interest, there is an item in the newspaper mentioning the licence for the Duke of Wellington, Shepherd St, Christchurch transfered from Samuel MASKELL to John JAQUES:
Sunday,  Jan. 17, 1858
Publication: The Era

John JAQUES died 19 August 1858: here is a copy of his probate.

Oh, I can't attach a copy here.


"JAQUES John Effects under £600.
17 November Letters of Administration
of the personal estate and effects of John
Jaques late of the sign of "The Duke of
Wellington" Public House Tenter Ground
Spitalfields in the County of Middlesex
Victualler deceased who died 19 August 1858
at the same place were granted at the Prin
cipal Registry to Prudence Jaques of
"The Duke of Wellington" Public House
aforsaid Widow the Relict of the said De-
ceased she having been first sworn."

You can search for wills and probate here:
https://probatesearch.service.gov.uk