To add a but more to the other fine answer:

1. There is a set and published salary range for Senior Lecturer/Reader at each UK University, and they are all close to the same. At my (and other) UK Unis this is grade 9. If you search for the University in question's salary scales, you can see the grade 9 range and that is what you have to work with. They cannot offer you more without making you a professor and making you a professor would be strange indeed (see 2)

2. Untenured assistant professor to reader is really quite a big promotion in UK terms. You started at what we'd call permanent Lecturer and you've skipped a whole academic rank (Senior Lecturer) that most people would spend a few years at. As a reader you may be asked to serve as head of department, or on higher level University committees, etc. Yet the service jobs wont be as onerous as those for being a professor. You might get a further teaching buyout due to taking on some of these service roles. You'll have less teaching than the US anyway. As you are in a promoted position, more funding opportunities will be available to you via the research councils as you'll look senior on your CV. You also have the ability to apply for promotion to professor in your next promotion round (or as soon as you feel like you have the evidence). Reader is quite a good position to be in.