Claude, buddy, uses hostingpics.net. Which site is in french.
Give it a try! Also read text in italics.
Again, again, again and again the show/hide extension for known file types issue.
What you encounter has nothing to do with fonts or downloads. Be it here on dafont or elsewhere. It has to do with the settings of your operating system and whether or not you understand your operating system.
Seems you want to run before you can walk.
buddy85 said 
... Do you mean to say you can extract a font from the css? I am editing the document in illustrator, so this where I'll need to import it. ...
No. In the source of the web-page a css file is mentioned. Open that css file and search for times and you will find a link to where the font(s) is(are) located on the The Times website.
Exactly the same principle as when you were to include a font on a web-page you were making.
The images you are showing seem to be copies from the web site of The Times. Is that what you are after? Or do you want the font the newspaper actually uses for printing?
If so, go to a news stand. Buy The Times. Scan some headings and some body copy in high quality. 300 dpi minimal and post those scans.
Only then we can see the difference between the two and which font comes closest to the print version.
There is a lot of confusion about the TimesModern as there are several with the same name but all slightly different.
Which one are you after?
The ones (Regular and Bold) The Times is using at the moment for its on-line pages can be found through their /d/449/styles/main.min.css file as .ttf, .woff and .woff2. These are very simplified letter shapes, look at the rudimentary serifs, and imho can not have much in common with the font used for print. But I can not check that as The Times is not sold within 250 km from here.
Both .ttf files show an error message when opened with Windows font viewer and must be opened and then saved again in a font editor to overcome this. Whether the same goes for an apple I don't know.
The one you mention as made by Elsner&Flake is not for sale anymore but it's offsprings are having a good time out there in the wild. It may be a font that is close to the one used by The Times for print. But then, may be not.
So best first tell us which version you are after. And if that happens to be the print one then scan a few headings and post them here. You can use the bbc [IMG] code.
Type bump in the reply field. But not within 24 hours.
I am with you as far as the A and R being modified but not the Veneer however close it is.

Also around as QK-Washington. Also P22.
My problem?
My problem is that there are people around that show no respect whatsoever for the work done by others.
My problem is that there are people around that just take anything they want without considering that it is someone else's property.
My problem is that there are people around that think that that is normal.
My problem is that there are people around that that have no clue what they are doing and then proudly name themselves clueless. How dumb can one get?
Ever thought about that making a good usable font can take months, working many hours a day? Guaranteed not. As thinking requires having a clue ... and you, clueless, don't have a clue.
Why shout?
Yes, not all software improvements are improvements. Same here on dafont where the new google image can cover a (small) posted image.
Well, excuse me clueless. So it was not your boss who told you to do it. You did it all by yourself. Knowing that your boss would not want to pay for other peoples work so he/she can make more money him/her self. Or did you just assume so? And did you also assume that someone somewhere would type that letter with that typeface and turn the outcome into a PDF and then send it to you for free?
So it is not only your boss who, you assume, wants to live of someone else's pocket. It is you too.
Tell me clueless, is Tennessee really the state of little cheats and thieves as rumor has it?
All times are CET. The time is now 03:33