I have now experimented a bit with this and I can confirm: FT runs stable and without trouble on Chrome now, be it a bit slower than what I'm used to. And indeed, all the video ads using flash are replaced with normal 'static' ads via Chrome. Flash memory usage doesn't explode anymore, either.

I can fully recommend to switch advertising companies or to renew the agreement with the advertiser so that video ads are blocked. Here's why:

I must urge FT's tech to seriously look into this, as the trouble still is around and I get the impression that tech is still thinking it's only a few individual advertisements, and not getting closer to a fundamental solution yet. Remember that the patience of the audience is not everlasting. Soon there'll be no people left to advertise for...
In an attempt to try to help a bit, I've done some testing. I can confirm: it's probably not just a single advertisement, it's probably the whole Flash video advertising setup. As said, I've experimented quite a bit with this recently. I have visited FT in the last few weeks via at least 20 countries, using at least a dozen different computers, with even more browsers and flash versions installed (and yes, updated a few to the latest version, where possible and where allowed). I've 'seen' hundreds of different video ads (if they actually ran. And if they ran, they usually already froze my browser so that only the extremely loud audio sounded), varying from Norwegian biological yogurt to Chinese deals on household electronics and American deals on buying stock and a better life. The problem remained, until I killed the Flash player. Which in turn may kill the browser or the whole computer. Which will eventually be killed anyway if Flash isn't killed on time. Only weakness: only Windows computers were used. The good news is that it was both 7 and 8.
And... as soon as a new thread is opened, Flash is being activated again, causing all trouble to happen again. That makes testing not only a very frustrating activity, but also a fast one: if multiple threads are opened simultaneously in several tabs, it all crashes even faster!

Now for the catch: there's no point in making screenshots. Either the memory is too much taken by Flash to allow other programs to operate properly, or I have the advertisements killed with the Flash player, so only grey areas appear where the videos used to be. This only helps proving my point partially: it's the video ads using Flash. It doesn't prove that it's not just one specific video ad, though. That was proven by the browser freezing anyway when the many different advertisements did load and started playing.

Now that my computer froze three times today when on FT, I actually came here to write a farewell note (with pain in my heart, but still), as visiting FT is a hazard now (and there's little progress on the matter, it seems) : either it makes my computer crash (which is unacceptable) or it makes my eardrums crash (or annoys other people if I don't have earphones in, both are also unacceptable). Chrome is by far not my preferred browser (and not even allowed on all the pc's I use), so it's not a solution, more or less a highly uncomfortable workaround. Anyway, I can't afford to have damage done to my digital assets via an avoidable hazard.

I am a professional IT person with over a decade of professional experience (including high competence in testing) and I can advise you: I'm fairly certain it's Flash via the video advertisements which causes the trouble (I need more and broader testing to be certain, but all points in this direction). I would double check what you've changed about 4 or 5 months ago in your code that may affect advertisements or Flash usage. Check what has changed with your advertisement agreement and check if the advertising company changed something on their side. Check if there's anything else using Flash on FT besides the advertisements. And either get a new agreement where no such video ads are used anymore, or switch advertising company if it's not possible via the current one.
Also, it's not necessarily someone's fault. It can be a combination of factors, like specific variables or pointers in the code in combination with a Flash video causing a memory leak or putting loading a video in an (infinite?) loop.

I hope this helps!

ps. I also got the Uber voucher smacked in my face the other day. As I was on a company laptop, I ran three different anti virus and anti malware programs. To be sure, I consulted the principal information security architect for a second opinion. This laptop is as clean as can be. So... please check again with your advertisement company and also check your own servers: if it's not an aggressive advertisement then some server might be infected...

pps. I haven't encountered the IE hazard, as I don't use IE if I can avoid it, but if this is only encountered via FT, as most state, then it'd be wise to have the servers checked for any malware or viruses, just to be sure, especially also given the Uber-voucher encounter. Contact the web-host to have this done. And, of course, depending on the result, check all third parties involved, especially those responsible for advertisements.