I have an offer from ucl for 'Mechanical Engineering with business finance'. However, I am starting to become a bit doubtful about whether I want to study engineering or economics. Now, I know ucl's economics course is better ranked and more competitive. I just wanted to know what are the chances that (if later I want to) ucl would allow me to change my course.
Thanks in advance.
Is there a particular reason you want/need to pursue economics instead of engineering? The latter is perfectly acceptable for any generic grad scheme as economics, and you'll have a sufficient (better, possibly) numerate background to "hop fields" for a masters/PhD in most circumstances on the academia side of things. If you seriously believe you won't enjoy and do well in engineering then I'd recommend you take a year out and reapply during a gap year to a full set of economics courses and focus your efforts on that, if this is that case.
However if you're just considering it because you think economics will have better prospects, the courses will be ultimately the same in terms of job prospects - in fact engineering has the benefit of giving you much more flexibility in the paths you can pursue. Economics is only relevant if you specifically want to continue in that field as an academic, and as above there are ways into it from engineering. For generic grad prospects, the roles that consider "prestige" they only care about the university overall - they won't care one jot about your specific subject (aside from potentially "numerate" vs other, and both courses fall into the former category).