No place is represented more in American naming trends than the British Isles. Sure, you get girls named India, Kenya, China and Holland and boys named Rome, but The British Isles are consistently the most represented.
Since 1969, 21 boys and 158 girls have been named British.
268 girls have been named English, starting in 1961.
190 boys have been named English from 1899-1993.
99 boys and 1333 girls have been named Irish, starting in 1924.
Nobody seems to have ever been named Scottish or Welsh (at least fewer than 5 per year, which is the lowest number the Social Security Administration records).
Those seem to be the only nationalities represented aside from German, of which there have been 8324 boys named since the 1880s. German, though, is usually a Spanish name; a form of Germanus (English form is usually Germane).
Of the countries themselves, between 1916 and 2010, 178 boys were named Ireland. The first female Ireland wasn't born until 1993, but since then there have been 3729 of them. It also gave rise to the forms Irelyn, Irelynd, Irelynn, Irelynne and Irlanda. By far the most popular Ireland-related name is Erin (a poetic name for Ireland). The name is used from 1880 (when the SSA started keeping track) all the way to 2011. In that 131 years, there have been 306,332 girls named Erin. 1983 was the peak year for that name's popularity.
Starting in the 1970s, there have been 427 girls named Britain. There have been 529 boys named Britain since 1969, and a lot more named Briton, Brittan, Britten, Brittain, Britan, Brittin, Britton etc. Starting in the late 1980s, following in the footsteps of the popular name Brittany, there have been 10 girls named Britannia (Latin for Britain) and 15 Britannicas (like the Encyclopedia!)
Since 1976 there have been 83 girls named England. As for boys, 1983 was the only year any were named England, and then only 5 of them. 639 girls have been named Anglia (a Latin name for England) since 1949, but this is probably a typo for Angelia.
Since 2000, 86 girls have been named Scotland. Scotland also gave rise to girls named Scotlyn, Scotlynn and Scottlyn. The first boy Scotland was recorded in 1976, and there have been 152 since then. Scotia, a Latin name for Scotland showed up 4 years for girls: 1974, 1992, 1994, and 2006. There have been 24 Scotias in all. Caledonia is a Roman name for Scotland, which is a little more popular for girls: there were 5 born in 1900, then none until the 2000s where there have been 47 so far.
Between 1914 and 1968, 48 boys were named Wales. There have been no girls named Wales, but since 1963, there have been 3423 girls named Cambria, which is a Latin name for Wales.
As for cities, London is by far the most popular, with 17,274 girls named after England's capital since 1963. 6134 boys have been named London, starting in 1886. Both have many recorded alternate spellings including Londen, Londyn, Lunden, Londin, Londynn etc.
Other British cities represented are:
Aberdeen (girls = 45 since 1913, Boys = 0)
Brighton (girls = 695, boys= 1381 both first appeared in the 1980s. The girls' names have the variant Brightyn appearing in the 2000s).
Bristol (girls= 2162 since 1976, boys = 389 since 1915. The girls' names also have the variants Bristal, Brystal, Brystol and Bristyl. The recent popularity is almost certainly due to presidential candidate Sarah Palin's daughter, and now reality tv star Bristol Palin.)
Brixton (first appeared for girls in 2009-- there have been 24 since then. For boys, first appearance is 2001, and there have been 249 in all.)
Cambridge (girls: 17 since 1992, boys: 21 since 2001)
Derby (girls: 5 in 1955 only. boys: 29 since 1991)
Dublin (girls: 33 since 2006 + 5 Dublyns, boys: 150 since 2003)
Sheffield (boys: 65 from 1914-1968, girls: 0)
There are other places like Bradford, Preston, Boston, Dudley, York, Chelsea, Jersey etc. represented in names, but these are more likely either popular because of surnames or places in the USA named for the places in Britain.