- The exact claim, "...completely ignored...", became untrue the day after this post was published. There were a few clips on the BBC 24hr rolling news channel around the time the post was published, but the BBC had nothing online about the protests anywhere until the following day, and nothing on any regular scheduled news broadcasts.
- There is evidence for a reduced version of the claim. The BBC's coverage was limited to small slots on three relatively niche news outputs - its 24hr news channel, Radio 4, and regional (not national) London online news. The BBC acknowledge that they did not provide "extensive" coverage, as a deliberate editorial decision. It wasn't "completely" ignored - but most BBC news consumers would have seen and heard no coverage.
- The photo used in this post was misleading, from a different, larger protest on a similar theme, from 2011 (demonstrated in Oddthinking's answer)
- The rest of the claim is largely true, although it's debatable whether the number of protesters was definitely above 50,000 (see georgechaloub's answer)
At the time the post was published, there was nothing on the BBC website about the protest, and no other BBC coverage anywhere except a few clips on the BBC 24hr News channel (see sources below). There were other media outlets which had covered the protest in their mainstream reporting (the Guardian, and ITV tea-time news are given as examples in one article).
There was, later, some limited BBC coverage:
It seems there was no coverage on regular BBC TV or radio news, and nothing on the national sections of the BBC news site.
This is based on the BBC's reply sent to many of the people who complained about the coverage of this protest, quoting unnamed "senior editorial staff at BBC News", an example of which can be read here, with a key part copied below:
We covered this demonstration on the BBC News Channel with five
reports throughout Saturday evening, on the BBC News website on
Sunday, as well as on social media.
They go on to acknowledge that this falls short of "extensive coverage":
We choose which stories we cover
based on how newsworthy they are and what else is happening and we
didn’t provide extensive coverage because of a number of bigger
national and international news stories that day, including the
escalating crisis in Iraq, British citizens fighting in Syria and the
death of Gerry Conlon.
This is the BBC national news homepage as it was at midnight after the protests, to give some context as to what the competing stories were. It appears to contradict the BBC's statement - there's actually almost nothing about Iraq or Syria (just one story, low down, about a family's response to a Jihadi video, and a mention in an "in the news" roundup article). Source: