A number of British sources have reported on Mark Pagel's research into the half-life of words. If there is a new paper by Pagel, I haven't seen it. This seems to be a rehash of the University of Reading prof's 2007 paper.
There are just so many things wrong with this reporting. To call words 9,000 years old (the article hints they could be 20,000 or even 40,000 y/o - yikes) "English" is just senseless. English began about a thousand years ago, according to convention. Of course that Old English came from an earlier language, which in turn came from an even earlier one, but we have to drop the idea of "English" pretty quickly. Even "Indo-European" would be a stretch, but there are at least some folks who would call that barely within the PIE fence. To talk about time traveling and playing Scrabble with Stone-Agers is meant to be amusing but is still too mixed for coherent thought. They have to sell newspapers, I know, but this is well beneath the standard of any reputable science section.
The research is essentially this: some words change more slowly than others, and we can recognise resemblances across time and geography. This has long been known. The Swadesh list consists of common words that have been shown to be more stable over time. Pagel has tried to quantify this by estimating the half-life of words and projecting backward what words used in 7000BCE have direct descendants of similar meaning today. He also notes some words which are so divergent in meaning between languages as to be considered unstable, and on their way out in the next thousand years or so. The words Pagel believes are most stable are similar to Merritt Ruhlen's list - well, there's a surprise - the smaller numbers, personal pronouns, and parts of the body predominating.
Well fine, so far. Even historical linguists who believe we can't trace back with any confidence more than 6000 years would likely agree that the principle of stability is as likely in the Swadesh words in the 6000 years before 4000 BCE as the 6000 years after. "I," "we," "two," "five" likely changed as slowly in the old days as in the new. If we could make a tracing back 9000 years, those would be our first suspects. The problem is, those words are already just barely recognisable to us over 6000 years.
For example, German Wasser, French eau, Latin aqua. Does the connection jump right out at you? No. You can trace all those back to PIE *akwa- but it's rather painstaking to get there. That whatever word they used for water in 7000 BCE, if we could know it, might be intelligibly connected to *akwa- I grant. But the point is we don't know it. Other language families suggest that something like kwa, akwa, okwa, okho might have been that word, but we are a long way between stepping-stones here.
Simplest answer. You could quickly learn to understand and be understood 400 years ago, if you like that time-travel idea. 800 years ago, maybe. 1200 years ago, you are learning a foreign language, noting occasional curiosities that make you suspect it's related to English. 9000 years, 20K, 40K? No chance.
If you're planning on time travel, work on your gestures instead.