I'm not sure if any of this will help, as I only have Beaconsfield marriages, but here goes!
The 1761 marriage of Francis & Elizabeth doesn't give any extra info, other than they married by licence. I don't know if it would be worth trying to obtain a copy.
A quick look on Family History Online adds that Francis was a bachelor 'of this parish' and Elizabeth a spinster 'of this parish' and that the witnesses were John Turner and John Grove.
Interestingly, there is a marriage for a John Turner in Beaconsfield -
19 Oct 1739 John Turner of Burnham & Elizabeth Hutchins.
Could these be Elizabeth's parents?
Another marriage in Beaconsfield -
12 Jan 1734 Edw. Woolhouse & Mary Harris
Possibly Francis' parents?
It's frustrating without the Beaconsfield/Burnham baptisms to follow this up, so hopefully someone else will be able to help with the baptisms.

Were any of Francis & Elizabeth's children named after these possible parents?
Jill