MSc Public Policy UCL vs MSc Regulation LSE vs MA Public Policy KCL

Please, I would like some help and advices.

I'm an overseas student. I study law during my undergraduate years. At first, I intended to apply for LLM, but I've been granted a full scholarship to study public policy or regulation. I think it's a good opportunity, studying abroad; hence, I've decided to take this scholarship and apply to these schools instead of pursuing on an LLM.

Now, I got an offer from them, and I can't decide which ones will be the best fit for me because I don't have any experience relating this field. It will be my fresh start. I'm quite keen on exploring this field as well. I took a look at modules and courses. But my main concern is about my future prospect.

My future prospect is that after finishing this degree, I'll do an LLM next. My aim is to reapply for Oxford MJur (I was rejected this year. Heartbroken. I think taking some time, building up my profile would help. Am I too naive?). If not, I still would like to do an LLM at other universities or work for private sectors or big firms in the future. I'm currently working for the government, and I think it's not a place for me due to the system. So, studying public policy would not that helpful in my case.

This is why I would love to ask for advices please. Which program (MSc Public Policy UCL vs MSc Regulation LSE vs MA Public Policy KCL) is the most suitable for my situation?

Please be my guidance or knock some senses into me. Thank you so much for your help.