It's hard to measure reputation, really. And I see, that's the main dilemma for you. I've got an offer from Warwick and didn't apply to UCL but I am not very biased since I am still not 100% sure what uni to firm:
UCL's overall reputation is really good. They've existed for many more years than Warwick and the foundation date of a university does play a role reputation wise. So UCL's got the edge here. Warwick is still kind of new but there is almost no other university that has gained so much reputation in such a short time. And of course this is only an estimation, but I am sure that Warwick has the potential to to become even better in the next 10/20 years. I don't have the figures anymore, but there was a statistic that showed the annual expenditure of various Economics Departments. Warwick invested as much as Cambridge and LSE. This doesn't necessarily mean high quality but it does show that they take things seriously and that they are really expanding their economics branch. And employers have realised it.
I can't speak for rthe quality of UCL's course as I didn't apply there and hence didn't go to any Open Days to talk to the students but I assume it's not better than Warwick's but not worse either. They are about equal. Both are very mathematical. It depends on what modules both unis offer and what you prefer. Warwick has a huge variety and I assume UCL has the same but you might prefer some optional/mandatory modules at UCL or Warwick. So take a look at that.
Overall you can say: The reputation is about the same. There might be the general crowd that have never heard of Warwick but heard of UCL because it's been very good for a longer time than Warwick, but if employers see them as equal (don't think they prefer Warwick students), it means a lot. Maybe Warwick has a better career service and that's why they secure more interviews but that doesn't mean that employers prefer Warwick
Oh and the London factor doesn't play a big role. What I mean is, you won't have an actual advantage when living in London. There are as many firms coming to Warwick as firms are coming to UCL. It's just more comfortable living in London since all the firms are around you, that is if you secure an interview you won't have such a long way to drive
So I'd say just go for the one where you prefer the course, that is, the modules. Reputation-wise you can't make a mistake
Sorry for the essay and for the language. My English has been getting really bad lately