Hello again Bob,
do you know the web sites that Sue as, She's a Famous Gipsy Scholar, I suppose you do, but encase you do not, look up the Romany Genes web sites, there are lots of references to the Mills Family on there pluss many names that lived along side them in all those old stopping grounds from long ago, you may evan write to Sue, I'm sure She would put you right on who was who, or if these Mills where related to those Mills, you can not take nothing for granted, you must just keep trying and follow every lead, these below are just little extracts from Sues websites, find those sites for all the full information's, 
Web Sites
Romany Genes ........    S.J.Day
Romany Genes 2 ........ S.J.Day
Romanies Reunited.......S.J.Day
1861* Hemyock Devon
Cornelius Mills abt 1808  Sturminster Dorset Hd/Tin man/Basket maker 
Cinderella Mills abt 1811 Southampton Wife   
 Susan Mills  abt 1837  Sparkford, Somerset Daughter    
 Rosetta Mills  abt 1844  Chinley, Devon Daughter    
 Matilda Mills  abt 1847  Brad, Devon Daughter    
 Louisa Mills  abt 1850  Staples, Somerset Daughter    
 Joseph Mills abt 1852  Gothurst, Somerset Son  
1861* Hemyock  County/Island: Devon  
Cornelius Mills 53  hd Tin-man/basket/Maker b Sturminster, Dorset
Cinderella Mills 50  wife Basket/maker b Southampton
Joseph Mills 9  son  b Gothurst, Somerset/Basket/maker
Louisa Mills 11  dau b Staples, Somerset,
Matilda Mills 14  dau b Brad, Devon/Basket/maker
Rosetta Mills 17  dau b Chinley, Devon/Basket/maker
Susan Mills 24  dau b Sparkford, Somerset/Basket/maker
1851 CENSUS LONG SUTTON HAMPSHIRE
ALL LISTED AS TRAVELLERS LIVING IN TENTS.
Ann Mills abt 1779 Herriard, Hampshire, Head 
Frank Mills abt 1811 New Town, Hampshire, Son 
Frank Mills 1838 Grewell, Hampshire, Grandson
1861 Census:Wandsworth:Surrey (Tents and Caravans)
(Palmers Field)
Joseph Mills 40 hd b Petersfield, Sussex
Naomi Mills 25 wife b Dorking, Surrey
Aaron Mills10 son b Chaley, Sussex
Eliza Mills 5 dau b Frogarts Heath, Kent
Susan Mills 3 dau b Wimbledon, Surrey
 1891 Census*Hartley Wintney Hampshire*
Gypsies in tents and Caravans Hazely heath common
(all Gypsies or Hawkers.Note all in tents except Bulcher Buckland who had tent and a caravan!
 Mills 6 weeks  son
Evanglas Mills 2  son
Maud Mills 4  dau
Sabina Mills 22  
Thomas Mills 21  
1861 *Census* Middlesex : Hammersmith (In Tents) (Large camp )
Waste land on the West Side of Latimer Road called the Gipsies encampment)
*
Francis Mills 50  clothes peg maker b Newham, Hampshire
Francis Mills 24  son bGroole, Hampshire
Henry Mills 17  son b Sutton, Hampshire
Mary Ann Mills 21 dau b Weston, Hampshire
1881
Caravan & Tent Birkbeck Estate Woodford Essex 
Moses Smith  65  b Weathampstead Hertford  Hd Gipsy 
Fanny Smith  64  b Leicester Wife Gipsy 
Fambridge Smith 17 b  Loughton Essex Gipsy 
Ambrose Mills 19  g/son  b Hertford   Gipsy 
John Mills  9 nephew b Loughton Essex   Gipsy 
Galouse Mills  9 b Epping Essex  Gr/son Gipsy