Your introduction is mostly ok, with a few corrections.
재이슨이 입니다 -> 제이슨입니다.
(그리고) - > it's not wrong but I think it is not necessary.
영국에서 옵니다 -> 영국에서 왔습니다 (오다 can mean "come from", but usually in past tense).
뵙겠슴니다 -> 뵙겠습니다.
드십니다 -> 드립니다.
"안녕하세요? 저는 제이슨입니다. (그리고) 영국에서 왔습니다. 처음 뵙겠습니다, 잘 부탁 드립니다."
You can mix in some less formal sentence to make it smoother.
"안녕하세요? 저는 제이슨입니다. 영국에서 왔어요. 처음 뵙겠습니다, 잘 부탁 드려요."
When talking about someone who's already at his destination, Koreans always put it in past tense (Korean past tense also has the sense of present perfect "has come").
Present tense is used only for some instance of travel or migration happening now.