Shinzo Abe was quoted late last year as saying that the TPP was essentially meaningless without the United States, and I think his (probably unintended) forthrightness reflects most of the conventional thinking on the subject at the moment.
The sizes of the economies involved are only a part of what made the TPP a viable proposition for its partners - and maybe not even the biggest part. As the article you linked points out, in the grand scheme of Asian geopolitics, the TPP was an attempt to limit China's ongoing attempts to build a parallel network of economic and diplomatic institutions that would eventually supplant U.S-sponsored institutions and trading relationships. Japan's geostrategic aims were closely tied to Washington's in this regard, which is why they were amenable to the prospect in the first place - the rapid trajectory towards regional hegemony that Beijing has experienced over the last two decades forced Tokyo to reconsider the importance of its remaining tariffs and protectionist measures within its national strategy.
To effectively fulfill its geostrategic purpose, the TPP was meant to draw in Asian countries like Malaysia and Vietnam, and ensconce them into trade partnerships with the United States and Japan that would act as a bulwark against growing Chinese attempts to exercise outright economic, military and diplomatic dominance in the East and South China Seas. The economic purpose of the deal was to liberalize trade,create common administrative and legal frameworks and generate growth across all its participating nations, of course, but the geostrategic element was equally important - to Tokyo, to Washington and to regional capitals hoping to stave off the prospect of being dominated by Beijing. And both the economic and geostrategic elements of the deal were completely reliant on the United States - the economic concessions and gains made by all parties across the long negotiating period were *entirely* predicated on gaining mostly free access to the 350m relatively wealthy, active consumers within the United States. And, likewise, the geostrategic aims of the deal were predicated on certain things. Namely, the comprehensive national power at the disposal of the United States in the Asia Pacific - the United States Seventh Fleet stationed at Yokosuka, the 40,000 U.S military personnel stationed across Japan as a whole, the Arleigh-Burke class destroyers conducting Freedom of Navigation patrols across the First Island Chain, the litany of U.S air assets at bases across Japan, South Korea and the Pacific Islands and the combined diplomatic, economic and military infrastructure across Asia that would allow Washington and its allies to confront Beijing with the threat of *forcing* compliance were the nations involved in the TPP to be threatened by Beijing for their participation or unwillingness to accede to Chinese aims in Asia.
As I said, every trade deal is *more* than just a trade deal. With the E.U, the geostrategic aim was to unite Europe as a bulwark against the prospect of strategic irrelevance - and with the TPP, it was to combat the rise of China as a power seeking regional hegemony in East Asia. If either Britain or Japan were to restart the TPP as it was originally negotiated, one of them would have to step into the shoes of the United States in order to keep the economic and geostrategic logic behind the deal alive. And neither is capable of doing so - especially the UK. As I mentioned, the UK's domestic market isn't big enough to make opening up an attractive prospect to Japan or other participating nations - and Britain has very little to offer the countries involved in the deal in terms of sector-specific expertise needed by all members, whether developed or developing. And from a geostrategic perspective, the UK can't give critical mass to anything anywhere - what Hanoi wants from a TPP-level partner, for example, is a willingness to stand up to Beijing and to protect Hanoi's sovereignty with force if necessary. Would Britain be willing to stand up to China to protect Vietnam's claims in the South China Sea ? London doesn't even whimper when Beijing cracks down in Hong Kong. And would it be willing to employ force to dissuade China from disrupting the trading relationships created by the TPP? The Type 45s can't even chug into the Persian Gulf without breaking down, there are almost no British assets on station anywhere east of Suez, and the whole prospect of the UK independently standing up to the juggernaut that is the PLA is utterly laughable - that sort of potency died in 1945, and has never returned since.
Only America could fill those roles. Which is why the TPP sans America is just a pipe dream, more or less. That's not to say that the countries involved couldn't slowly, painfully try to create a new deal with far fewer concessions and much-reduced geostrategic ambitions, but the UK can't really give critical mass to anything, is my point. I don't think you meant it that way, but my frustration is that a lot of people in the UK seem to think in that way - and that's just *wrong*.