Kieron - don't know about everywhere else, but in the UK the third part of the Disability Discrimination Act has just come into play and most websites providing a service HAVE to be compliant, so there's pleanty of resources around to help with accessibility.

The main things are: make the HTML valid and check it with a validator such as http://validator.w3.org/, which (certainly in the case of XHTML 1.0) includes a check for alt tags for all images. Keep the contrast in colours strong, separate content from presentation by using style sheets, and try out an accessibility validator such as http://wave.webaim.org/.

Usually it's basically a lot of tidying up rather than a redesign. Good luck!