Hello Marko,
Pallot's has a marriage of Jas Pearce (b) and Hannah Hopkins (s) at St. Paul Hammersmith in 1834. Hammersmith seems to be geographically close to Fulham.
The IGI has a Hannah Hopkins christened 16 Aug 1807 in Burghclere, Hampshire. Parents listed are Richard Hopkins and Dinah.
The Batch Number for this entry also lists a Martha Hopkins with parents Richard Hopkins and Dinah, christened 25 Jun 1809.
Caution is needed with this next item because it is not an extracted record, but the IGI also has a marriage of Richard Hopkins and Dinah Bowles on 23 Dec 1805 in Burghclere, Hampshire.
Hope this Hannah turns out to be yours.
Regards,
Polarbear