Hi,
I've recently started the Access course you're talking about, and the English diagnostic test is really nothing to worry about. Although I do know of colleges that do computerized tests, ours were on paper, and were literally a choice of 1 of 4 topics to write a brief passage about (about 150/200 words I think).
Like you, I had been out of the education system for a long time (+20 years on you in fact), and I went into panic mode at the thought of tests before I had even started the course, but there really was no need. As long as you can show that you can read the question and write a half sensible passage, it will be plain sailing.