As a number of you are American, I thought the following might prove interesting.
There are three Warringtons in America: one in Escambia County, Florida, named after a person, Lewis Warrington, and two in Pennsylvania, named after the town in England. (For British readers: Pennsylvania was founded in 1682 by the English Quaker, William Penn, who accepted a large land grant in New England in payment of a huge debt owed to him by Charles II. Throughout the eighteenth century, Quakers from all over England emigrated there to escape the religious intolerance of the period.)
The two in Pennsylvania are Warrington Township in York County (previously Lancaster County) and Warrington Township in Bucks County. (Bucks, incidently, is a postal abbreviation used in England for the county of Buckinghamshire.) Apparently, there is a claim by some that the York County Warrington is named for a town in Ireland, but I would suggest that the previous name of Lancaster County disproves this: at the time it was founded, in 1735, the English Warrington was in the county of Lancashire.
The Bucks County Warrington still has a strong Quaker tradition, as does the English Warrington, with both having early eighteenth-century meeting-houses set up within a few years of one another. The English Warrington meeting-house has, rather sadly, lost its quiet seclusion in Academy Place; now, Academy Street, a wide traffic-filled road, clips the front of its old school, behind which it hides.
For those wishing to look into a possible family connection, the Quakers in Warrington, England have a website, although bear in mind that they will have drawn in people from all around the area.
In searching in other areas, it may be useful to know a little of England’s historical geography. England is divided into counties, as, I understand, are the American states. Each English county is divided into Hundreds, and each Hundred is divided into parishes. Where a parish is particularly large, it may be further sub-divided into townships. Thus, if you were looking to trace an ancestor who you think may have lived in Bridge Street, you would look for records in Warrington township, in the parish of Warrington, in the Hundred of West Derby, in the county of Lancashire. (Do not be confused with the modern placing of Warrington in Cheshire, this was a political move in the 1970s and one which older Warringtonians have no truck with. See Friends of Real Lancashire.)
The county boundary between Lancashire to the North and Cheshire to the South was the river Mersey, so your ancestors could quite easily have popped over the river to attend the meeting-house if they lived on the south side. In this case, you would be looking for records from Cheshire. Parishes in Cheshire tend to be a lot smaller, those near to Warrington are in Bucklow Hundred.