Upvote:3
Since your passport was issued before the October 26, 2005 deadline, all you need is a machine readable passport (https://esta.cbp.dhs.gov/esta/WebHelp/ESTA_Screen-Level_Online_Help_1.htm#vwp4), it doesn't even require a digital photo. And according to Wikipedia, all British passports since ~1988 (though they may have issued old stock until 1993ish) have been machine readable so it would seem you are fine.
As @Gagravarr pointed out, the machine readable code is easy to identify. Should be a simple job to check.