The 1841 census (see below) I believe is Avies but Wilmshurst is a Maidstone name in 1851 so is Avies's surname Wilmhurst or Hearth (Hurst?) but I haven't found any further records of Bashemath Wilm Hurst (mum of Avis) as yet.....
1901
Avies Cox (nee Hearth) died in the Sep qtr of 1901 Shoreditch R.D, London with a stated age of 68.
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I have the 1891 but if I included it I used too many characters
1881 census
68 Rotherhithe Street, St Olave, Surrey
William Cox............ head........50............decorator .............Lambeth, Surrey
Avies.......".............. wife......... 47.........................................Maidstone, Kent
James..... ".............. son..........29......decorator..........Holborn, London, Middlesex
Francis Henry ".......son......... 20............decorator.......Birmingham, Warwickshire
Joseph.... "...............son......... 18............shop lad.........Birmingham, Warwickshire
Alice........ ".............. daur.........15............servant.......Southwark, London, Surrey
Elearer Albert "....... son..........4................................Islington, London, Middlesex
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1871 census
4 Terrets Court, Islington, London, Middlesex
William Cox............ head........40............furniture decorator.....Lambeth, Surrey
Avies...... ".............. wife..........38..........................................Maidstone, Kent
James..... ".............. son..........19...............servant footman... St Giles, London
Charles E ".............. son..........14.....furniture decorator....Birmingham, Warwickshire
Avies...... ".............. daur.........12.................................St Georges, Warwickshire
Francis H "..............son..........10....................................St Georges, Warwickshire
Joseph.... ".............. son..........7....................................St Georges, Warwickshire
Alice........ ".............. daur.........5............................................Southwark, Surrey
Christopher ".......... son..........3...........................................Southwark, Surrey
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1861 census
No 1 Court 32, Upper Tower Street, Birmingham, Warwickshire
William Cox............ head........30.............Japonner................Lambeth, Surrey
Avies...... ".............. wife......... 28........................................Maidstone, Kent
William J ".............. son..........11...........................................St Giles, London
James..... ".............. son..........9..............................................St Giles, London
Rebecca..".............. daur.........7....................................Birmingham, Warwickshire
Charles E ".............. son..........4....................................Birmingham, Warwickshire
Avies...... ".............. daur........ 2...................................Birmingham, Warwickshire
Francis Henry "...... son..........5 months........................Birmingham, Warwickshire
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* A japonner is someone who decorated objects/furniture. Japanning involved high gloss lacquer finishes on papermache and wood applied and finished by hand.
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1851 census
37 Cromer Street, Grays Inn Lane, Pancras, London, Middlesex
William Cox............ head........20.....................japonner..........Lambeth, Surrey
Avies.......".............. wife..........18..............................................Maidstone, Kent
William J ".............. son............1......................................Bloomsbury, London
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1849
William Cox marries Aveis Hearth at St Dunstans, Stepney, London, Middlesex....Stepney R.D, March qtr 1849, vol 2, page 375
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1841 census
Havock Lane, Maidstone, Maidstone, Kent
James Verrall..........................40................................................................
James....."...............................15................................................................
Chas........"..............................15.................................................................
Mary........"..............................40.................................................................
Bashemath Wilm Hurst..........40.............char woman................................Kent
Naomah..................."..............12................................................................Kent
Avis........................."..............10.................................................................Kent
Eliza........................"...............2.................................................................Kent
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Bryant