Hi again,
I've just checked the 1871 on Ancestry after looking at the transcriptions on the link I sent you.
Ian Hancock, the owner of the web site has transcribed their name as Haukswell in 1871.
Ancestry have confused the issue by transcibing the name as Hankswell, on the actual return it clearly reads as Haukswell.
I checked the family in 1881, ref. RG11/4871, folio 82, page 10. The name is now written as Hauxwell.
Quite sure you are already aware of all this, but it's sometimes reassuring to know that someone else is reaching the same conclusions!
I will keep my fingers crossed for the outcome of the certificate!
Kind regards,
Pels