I assume you are wanting to know how to say this in Korean right? If you are a beginner I would guess your classmates would be beginners as well, so you wouldn't want to say anything too formal or difficult for them to understand. Here is my suggestion: more simple: 저에게 연락하신 분들 죄송합니다. 지난달에 런던에 있어서 대답할 수 없었어요. 함께 공부 잘 해 봅시다. More Formal: 최근에 저에게 연락주신 분께 답변 못드려서 죄송합니다. 지난달에 런던에 있어서 대답할 시간이 없었어요. 함께 공부하면서 잘 지내고 싶어요. I changed the ending to "Let's study well together" it's a common phrase in Korean.

Your response sounds pretty good to me! "I'm sorry for not replying to anyone who has messaged me recently. I've been in London the past month and haven't had much time to reply." I don't know what kind of language program this is, but I would not write " I hope we can become good friends in the future!" since, if you don't know these people, you don't know if you want to become friends with them.