You could always look to the British royal family for inspiration;
Harry / Henry
Some other British namesakes include;
Horatio Nelson (could use either name here)
Isambard Kingdom Brunel
Alfred the Great
Robert the Bruce
Some very British names are listed below. Not all of these names are very commonly used, but I think most would be identifiable to the average Brit;
Alan / Allan / Allen (English & Scottish)
Alisdair / Alistair / Alastair (Scottish)
Archie (Scottish & English)
Colin (Scottish & English)
Gareth (Welsh & English)
Graham / Graeme (English / Scottish)
Hugh / Hugo (English)
Ivor (Welsh, Scottish & English)
Lloyd (English & Welsh)
Also, not sure how you feel about place names, but if you like them the following towns/cities might work as names;
I would be inclined to research a bit about any of place names though, as not all of them are very glamorous!
Albion, is one of the ancient names for England.
Saxon, one of the ancient people's of Brittain
Thane, a Scottish tital, I'm probably wrong but shakespheres Macbeth was the thane of Cordwall (?)
Thames (the river)
Alba (ancient name for Scotland) Alban
The lion is one of the symbols of Brittain so any of the Leo names.
George- patron saint of England
Andrew - patron st of Scotland
David- patron st of wales
Patrick - Patron st of Ireland
Stirling , as in pounds stirling
Thane of Cawdor.
I'm British and love the old-fashioned British names. My son is Stanley and I think our second (due January) will probably be Ted.
Other names to consider are Alfred (nn Albie), Arthur (nn Artie), Fred, Henry, Harry, Jack (as you mentioned), Frank, Edward, John, Winston. I quite like the idea of naming after a British city too - a modern, but very lovely choice would be London.
Novaberry knocked it out of the park! For what its worth, I like Jack.
Wow! Thank you for all the suggestions. I am going to research more about each name. I love the place names the most! London is one I have been thinking on for awhile.