Gosh, what a web! Not sure which is the most shocking

William the Cooper's son being only one of his 12 children to grow up to adulthood or his crusading mother upping sticks with a married man!
In 1837 on FreeBMD (Sep Qtr to Dec Qtr) there is just one Peter HAMPSON Birth Registration, in the Dec Qtr. In Preston. None in Preston in the next couple of years
As Hoole falls into the Preston District and as your Peter was christened in December 1837 in Hoole - that Birth Registration is perhaps likely to be his?
Because I'd lay bets that this is him :
1871 Census: Vessel "Medina" , enumerated in Ballantrae District, Ayrshire, Scotland
Master: Peter HAMPSON 34, Master, b Preston, Lancashire
Mate: William SMALLWOOD 33, Whitehaven, Cumberland
Fisherman: Isaac DREWERY 35, b Bradford, Yorkshire
Fisherman: Thomas QUAIL 51, b Whitehaven, Cumberland
1871 Census: 1 Hodgson Court, Whitehaven, Cumberland
RG10- Piece 5253 - Folio 70 -Pg37
Head: Elizabeth KYLE 36, mar, b Bradford, Yorkshire
Dau: Jane KYLE 17, unm, b Whitehaven
Dau: Mary Ann KYLE 14, b Whitehaven
Son: John KYLE 5, b Whitehaven
1871 Marriage: Sep Qtr 1871, Whitehaven
Peter HAMPSON
Elizabeth KYLE
1881 Census: 3 Building, Littledale Lane, Whitehaven, Cumberland
RG11 - Piece 5185 - Folio 68 -Pg34
Head: Peter HAMPSON 46, Fisherman, b Preston, Lancashire
Wife: Elizabeth HAMPSON 47, Fisherman's Wife, b Keithley, Yorkshire
Dau: Margaret HAMPSON 18, unm, no occupation, b Whitehaven
Son: John HAMPSON 15, no occupation, b Whitehaven
Servant: Mary Ann KYIELS 23, unm, Domestic Servant, b Whitehaven
Lodger: William KYIELS 9, Scholar, b Whitehaven
William may not son be a son, but another relative? 1891 Census: 1 Passage, Littledale Lane, Whitehaven, Cumberland
RG12 - Piece 4313 - Folio 49 - Pg22
Head: Peter THOMPSON 54, Fisherman, b Preston, Lancashire
Wife: Elizabeth THOMPSON, 55, b Yorkshire
Step-Dau: Mary A KYLES 34, single, b Whitehaven
Grandson: Peter CURWEN 13, b Whitehaven
Grandson: Isaac CURWEN 11. b Whitehaven
Note: Enumurated as THOMPSON (outside chance the TH is actually an H, but the P is there)The Grandchildren, issue of Elizabeth's dau Jane - who looks to be living next door with husband 2?Next door :
2 Passage, Littledale Lane, Whitehaven, Cumberland
Head: Charles SLOAN 36, Lamp Trimmer, b Hexham Northumberland
Wife: Jane SLOAN 36, b Whitehaven
StepSon: John CURWEN 17, Screener?, b Whitehaven
StepSon: Joseph CURWEN 15, Errand Boy, b Whitehaven
StepSon: Jonathan CURWEN 9, b Whitehaven
StepDau: Jane CURWEN 7, b Whitehaven
Son: Edward SLOAN 10 months, b Whitehaven
1901 Census: In 3 Rooms at 1 Hodgson Court, Whitehaven, Cumberland
RG13 - Piece 4891 -Folio 55 - Pg18
Head: Peter HAMPSON 62, widower, Fisherman, b Preston, Lancashire
Step-Dau: Mary Ann KYLES 39, Single, Fish Dealer, b Whitehaven
Cheers
AMBLY