How can publishers justify author fees for open access journals?
The short answer: some journals use author fees to offset the costs of running open access. 

Over the past decade, two practices have become more common together in academic publishing: full open access journals and author fees. The STM Report, an overview of STEM publishing, says the practice is growing in their 2018 edition, "3.2.1 Gold APC and author fees": 


  A growing number of journals make their entire contents freely available immediately on
  publication (full open access journals) using supply-side payments. Generally, these
  payments take the form of an article publication charge (APC) levied by journals at the point
  of publication, and it is up to authors (or frequently their research funder or institution) to
  make the payment.


In other words, traditional academic publishing has consumers (research libraries, universities, independent researchers, databases) paying for access to a journal. Open access means that the consumer side is effectively free. Instead, publishers recoup costs through  "supply-side payments" like author fees (known as a Gold APC [article publication charge] model) or institutional sponsorships (known as a Gold no APC model). Authors' fees have been around for decades in various forms, including "page charges," but this report and other commentators (like Kent Anderson) observe that these fees are on the rise again. 

What is involved in that cost? The report also includes an answer, under "2.9.12 Overall costs of peer review," emphasis mine:


  The notional global cost of peer review is substantial, albeit largely an estimate of academic time  devoted  to  it  rather  than  actual  cash:  an  RIN  report  estimated  this  at  £1.9  billion annually,  equivalent  to  about  £1200  per  paper  (RIN  2008).  The  Houghton  report  used  a slightly  higher  figure,  at  £1400  per  paper  (Houghton  et  al.,  2009).  These  figures  are  full costings, including estimates for the time spent by the academics conducting the review. The publisher’s  average  cost  of  managing  peer  review  (salaries  and  fees  only,  excluding overheads,  infrastructure,  systems  etc.)  was  reported  by  the  PEER  study  at  $250  per submitted manuscript (Wallace 2012).


So Cambridge University Press may be using the author fees to offset staff salaries, fees, overheads, infrastructure, and systems. Some of their cost is related to peer review, and some would be entailed in running the journal itself. Even if the actual peer reviews from experts are unpaid, all of the surrounding work incurs a cost. Given the RIN report and the PEER study estimates, that cost is somewhere in the hundreds or low thousands of dollars, pounds, or euros. 

How does that affect submission rates? As you might guess, some authors are turned away by fees. That said, these publications still tend to get submissions, perhaps because author organizations are able to pay the fees, because the pressures to publish outweigh the costs to the author, or because they are attracted to the open model for ideological reasons. In other words, the motivations vary from author to author.