My sister did her BSc in Econ at a top UK uni (LSE/UCL) and I did a BSc in Physics followed by a maths MSc at oxbridge. She interned in S&T, I am trying to get into quant finance.

A couple inputs:

1) The quantitative component of an econ degree is not sufficient for becoming a quant. Especially in the UK, where in my opinion university is less academically rigorous than in continental europe, an econ bsc is not a good enough preparation for a quant career (not enough maths and programming). And btw, in response to people who said that a good econ degree has more maths than a bad physics degree: they are not even close. If I compare my physics curriculum with that of my sister's BSc, they are miles apart in terms of how quantitaive they were and how much maths they had. Econ at BSc level doesn't go past vector calculus, linear algebra and some stats. They didn't even study integrals. However, I remember that my sister's degree had a lot of flexibility in terms of electives so you *might* be able to squeeze in enough maths to make it good enough for grad applications to MFEs. The best masters like imperial maths and finance and oxford MCF won't generally take you with an econ bsc but you will have reasonable chances for lighter MFEs like imperial RMFE and UCL computational finance, etc. Another options are computing conversion courses for quant developer roles (I know a guy with a business bsc who did msc computing at imperial and found a job as quant developer at BoA).

2) In my opinion, you cannot know at your stage whether you want to be a quant, you simply don't have enough data points to assess that because a) quants spend 95% of their time coding and I would guess you never spent enough all nighters debugging C++ code to understand if you actually enjoy doing it; b) the maths in high school is totally different than the maths at university. I was a rockstar in maths in high school (took part in maths olympads) but my physics degree has been quite a shock at the beginning (and quite an humbling experience too). Quants make less money than i-bankers and spend their days coding, which I think is a kind of occupation that would be enjoyable for a relatively small subset of people, arguably much smaller than those who might find IB or S&T enjoyable

3) I do know people with econ BSc who got into top MFEs (one at CMU, one at Berkeley, at one at Ecole Polytechnique in france after which he got a quant job at JPM) however they all did their BSc electives in maths and programming and the CMU guy also took several classes in maths as an outside student at a local university while he was working.

As I see it you have three options:

1) continue your bsc econ degree, which is arguably the best BSc in Europe if you want to do vanilla banking, and do IB or S&T. For instance, you could do some maths electives and shoot for more quanty S&T spots, like QIS structuring, exotics, etc. They are more enjoyable for 95% of people and you would make more than quants

2) Do your econ bsc taking as many electives as you can. Learn coding and do some projects, either as internships or on the side. Then you could take some classes in maths/coding as an external student or do a 1yr conversion course in CS or Maths (e.g. kings college has a maths conversion diploma) and apply for MFEs after that

3) Reapply as a transfer student for a maths bsc this year at imperial, lse etc

Personal advice: if I were you, I would focus 100% on route 1.