You said you wanted Beatles.
An obvious (and good) choice would be Paul's "Birthday" from the "White Album" (1968).
You said you wanted British invasion.
"Do Wah Diddy Diddy" (1964) from Manfred Mann is easy to sing and easy to play. It will get them up on the dance floor. Make it an audience participation number. After a couple of drinks, everyone will have fun with it.
2011 - 50 = 1961, her birth year.
If you have backing singers AND you can contract her name to one syllable, then Dion's "Runaround Sue" (1961) would be a great choice. It's a crowd pleaser, and uptempo.
Ex: If her name's "Florence", then it's "Runaround Flo"; intro: "The year Florence was born, Dion wrote this song about her..." She'll get a kick out of that.
If you can't contract her name, then the Shirelles' (Carole King's) "Will You Still Love Me Tomorrow" (1961) from her birth year would be a great choice.
I figure she will love you tomorrow after going to all this trouble for her birthday!