Were copies of The Times of London generally available for sale in 19th century Singapore? If so, how much did a copy cost? And how many days would the newspaper take to arrive in Singapore?
Until early 1871, when cable communication between Singapore and London was first established, it would take quite a while for information to travel between the two locations. Suez shortened the trip abruptly beginning in 1869, and there were many improvements to travel speeds throughout the century, but it was always measured in weeks.
That pretty much rules out there being a newspaper that's edited in London making its way to the general public in Singapore before 1871. At the same time it's sensible to assume that some might still be interested in reading a weeks old copy -- the governor, local business elites, etc. I've no idea what the cost would have been. (If I were to hazard a guess, I'd expect it to be in the ballpark of sending postage from London to Singapore on top of the newspaper's price. The GB Philatelic Society seems like a sensible place to try to get that info but from the looks of it they only have detailed records for postage costs within the UK. They might have pointers that aren't on their website if you reach out.)
After cable communications were established in 1871, it becomes theoretically possible to telegraph a newspaper's content (at a prohibitive cost) and print a local copy. But even then, automated typesetting was still two decades away from becoming more widely available. I'm struggling to picture how a local team, manually typesetting a paper, one page at the time, just for a tiny audience (74 Europeans in 1824; 2,445 in 1860), might make any economic sense. Therefor I'd suggest the situation didn't change materially -- that is, the paper wasn't available, except perhaps weeks later for the odd niche reader -- until the 20th century.
As a life long expat, I'd add that it's very unusual to find foreign newspapers abroad nowadays, and that insofar as I've experienced it, it already was almost non-existent in 1995. They mostly sell foreign newspapers at locations with international traffic such as airports, train stations, and harbors. Outside of those, your options are subscribing yourself or, if you're lucky, piggybacking on the subscription of the local Consular services venue, library, and university.