Job offer for UK Reader
Yes, UK salaries are currently significantly lower than US salaries at most ranks, and don't have much room for negotiation outside of a standard range.  The only exception to this is "professor" in the UK (which is often closer to distinguished professor in the US) where there's more latitude for higher salaries.

One major reason for the salary gap is that as recently as Summer 2015 the pound was worth nearly 1.6 US dollars.  If it comes back up then their offer would be more competitive, while if it goes down further then the offer will look even worse.

The only meaningful advantages I can see of a Reader over a US Assistant professor as a position is that there's more job security.  But presumably if you're a strong candidate for a Readership you shouldn't be too worried about tenure, and at many US schools this offer would get you tenure this year in a retention package.  (There are lots of advantages and disadvantages of UK vs. US which I won't get into, I'm only talking about the rank comparison.)