The short answer is that there is no specific time limit for Julian Assange to be tried.
In more detail: Julian Assange was granted bail in the extradition proceedings brought against him as the result of a European Arrest Warrant. He breached bail and so would appear to be guilty of the offence of absconding while on bail (see section 6 of the Bail Act 1976. That is the only outstanding offence being discussed (obviously he may be guilty of a great many other things, but we aren't considering those).
The Bail Act has a special mechanism that may be used for issuing a warrant for the arrest those who have absconded (see section 7). Such a warrant was issued against Assange.
Note that no proceedings under section 6 have yet been brought. It would be accurate to say "he is charged with no crime" at present. In the first of the magistrates' court proceedings this year his lawyers argued that since there was no underlying charge or trial in progress, section 7 was the wrong mechanism and the warrant should be discharged. The judge refused that application.
This is relevant because section 6 is unusual. It may be prosecuted either by "laying an information" (the usual way of starting a summary trial in the Magistrates' court) or as a criminal contempt of court. No information has been laid (it would seem) and there is a time limit of 6 months for doing so under section 127 of the Magistrates' Courts Act 1980.
That means, as far as I can see, the only consequences that Julian Assange could suffer would be committal for contempt of court, which is punishable by up to one month's detention (if tried by an inferior court like the Magistrates') or two years (if by a superior court). But there is, as far as I know, no specific time limit for contempt proceedings.
That is not quite the end of the story. If, reading this, you think that in theory there being no time limit for charging serious offences (and in principle holding a trial of any kind of offence, where someone has fled the jurisdiction), it is possible, though difficult, to force the authorities to drop their prosecution on the basis that their actions are an abuse of process.
This is what Julian Assange's lawyers argued in the second of his warrant applications. Their application was again rejected by the judge.
Having said that, what is true now may not continue to be true. The balance of proportionality may change. It is not impossible that he may be able to have the warrant withdrawn in the future, possibly the far future, but there is no mechanistic time limit as there might be in some jurisdictions.
The judgement refusing withdrawal of the warrant provides some useful background as does the second judgment dealing with the public interest.