a question about postgraduate studies

right- im writing purely out of curiosity

lets say someone did politics, or politics and philosophy, or politics and history- or something related to politics

LSE has a Political Economy MSC- the person with politics would be able to get onto that- right?

LSE also has a DPHIL in economics (again- ive tried economics, and prefer my different field, but im curious)- could they, with their unrelated degree, but related masters (provided a decent background in maths- I.E. As in A level maths/furhter maths)- get a PHD/MRES (which i think is
a doctorate) in economics- they say for their requirements:
"An upper second class honours (2:1) degree (or equivalent) in any field. Some preparation in economics, a strong mathematics background and evidence of research potential are essential. The goal of the MRes/PhD Economics is to train first class researchers. We will use all available information to assess research potential."

so in theory- could someone go from politics- an unrelated field to economics- to economics via masters/doctorate:
1. can they do this?
2. would they be able to work in stuff like banking/finance- or could they only work in academia/governmental stuff
3. would this be possible/achievable

(i am not doing politics/any of the mentioned areas of study above/i do not go to the LSE- my friend is just looking at the requirements- and i was curious when it said "any field"- i thought "quanititive degree" when i saw "strong background in maths"- but then they wouldnt say "any", they'd say "any quantitive degree"- if this the case- could one go on to do stuff like banking with this really good doctorate- despite lacking a relevant degree= i know Oxford/Cambridge want Economics degree, masters, specifically to do a doctorate- so why doesnt the LSE?)