That's is going to be a very long list of immigrants. These are just those who came before 1640 to New England directly from Wiltshire and doesn't include those who came after 1640, or went South or North of New England or those families who may have Wiltshire origins but moved to say Hampshire or some other county before immigration:
Andrews, William: Landford, Wiltshire; 1635 on James; passenger list only [GM 2: 1 :62].
Antrum, Thomas: Salisbury, Wiltshire; 1635 on James; Salem [GM
2:1:69-71].
Bailey, John: Bromham, Wiltshire; 1636; Salisbury, Newbury [MBCR
1:199, 266; SyTR 5; Phoebe Tilton Anc 179-81; TAG 29:110-13,
77:241-47].
Batt, Christoper: Salisbury, Wiltshire; 1638 on Bevis; Newbury,
Salisbury, Boston [Drake's Founders 60; Lechford 181; SyTR 1; MBCR
1:237, 277, 375; NEHGR 51:181-88, 348-57, 52:44-51, 321-22; Abel
Lunt Anc 175-255; TG 17:86-95; TAG 79:85-99].
Batt, Dorothy: Salisbury, Wiltshire; 1638 on Bevis; passenger list only
[Drake's Founders 60; Abel Lunt Anc 183].
Batt, Nicholas: The Devizes, Wiltshire; 1635 on James; Newbury [GM
2: 1 :200-4].
Batter, Edmund: Salisbury, Wiltshire; 1635 on James; Salem [GM
2:1:204-13].
Biddlecombe, Richard: Sutton Mandeville, Wiltshire; 1638 on
Confidence; passenger list only [Drake's Founders 57].
Blackstone, Elizabeth: Salisbury, Wiltshire; 1638 on Bevis; passenger
list only (servant) [Drake's Founders 60].
Blanford, John: Sutton Mandeville, Wiltshire; 1638 on Confidence;
Sudbury [Drake's Founders 57; SuTR 4; NEHGR 39:163; Dawes-Gates
1 :678-86].
Brown, Christian: Salisbury, Wiltshire; 1639; Salisbury [SyTR 1, 13,
14; HvBOP 7]. (She was the widowed mother of George, Henry and
William Brown of Salisbury.)
Brown, Thomas: Christian Malford, Wiltshire; 1635 on James;
Newbury [GM 2:1:435-38].
Butler, Giles: Marlborough, Wiltshire; 1635 on James; passenger list
only [GM 2: 1 :515].
Byley, Henry: Salisbury, Wiltshire; 1638 on Bevis; Newbury, Salisbury
[Drake's Founders 60; SyTR 2; MBCR 1 :237; Essex Ant 1 :20; NoyesGilman
271-74; NEHGR 42:308-9. 51:181-88, 348-57, 52:44-51, 321-
22].
Byley, John: Salisbury, Wiltshire; 1638 on Bevis; died soon after arrival
in New England [Drake's Founders 60; NEHGR 52:50; Noyes-Gilman
271-74].
Byley, Mary: Salisbury, Wiltshire; 1638 on Bevis; passenger list only
[Drake's Founders 60; NEHGR 52:50]. (She married Samuel Dudley,
son of Thomas Dudley.)
Carpenter, Thomas: Amesbury, Wiltshire; 1635 on James; passenger
list only [GM 2:2: 1 O]. (This passenger list entry is almost certainly an
error for William Carpenter.)
Carpenter, William: Amesbury, Wiltshire; 1635 on James; Salem,
Providence [Drake's Founders 56 (as "Thomas Carpenter"); NEHGR
159:54-68, 164:36-40, 296-97].
Church, George: Salisbury, Wiltshire; 1638 on Confidence; Newbury
(servant) [Drake's Founders 58; MBCR 2:46].
Cogswell, John: Westbury Leigh, Wiltshire; 1635 on Angel Gabriel;
Ipswich [GM 2:2:137-40; NEHGR 162:5-7].
Coleman, Thomas: Marlborough, Wiltshire; 1635 on James; Newbury,
Hampton, Nantucket [GM 2:2: 157-62].
Cottle, William: Landford, Wiltshire; 1638 on Confidence; Newbury
[Drake's Founders 58; EQC 1:336, EPR 1:438-39, 2:129-30; Hoyt 115-
16].
Coussens, George: Marlborough, Wiltshire; 1635 on James; passenger
list only [GM 2:2:221].
Currier, Richard: Salisbury, Wiltshire; 1639; Salisbury [SyTR 9; EQC
3:253; Pillsbury Anc 149-50; Philip Joseph Currier, Currier Family
Records of US.A. and Canada, Volume I (Henniker, New Hampshire,
1984); Philip Joseph Currier, Ancestry of Philip Joseph Currier
(Henniker, New Hampshire, 2000)].
Curtis, Zaccheus: Downton, Wiltshire; 1635 on James; Salem, Reading,
Gloucester, Rowley [GM 2:2:261-64; Kempton Anc 2:111-26].
Davis, Thomas: Marlborough, Wiltshire; 1635 on James of
Southampton; Newbury, Haverhill [GM 2:2:310-16].