I also have Tuesday 5th June listed as a Public Holiday in my diary - it's the Queen's Diamond Jubilee.
Most schools in Engald will probably be on half-term for the week before ie they'll break up on Friday 25 May and not go back until Wednesday 6th June. So your dates aren't off-peak, far from it I'm afraid. You'll probably find that if you can either bring your dates forward so that you are coming home on the weekend of Saturday 26th May or put them back so that you are not leaving until after the 6th June that prices will drop dramatically.
Alternatively, if you can't be flexible about your dates but you live north rather than south of Manchester, you might get a better price for flights from Edinburgh, Glasgow or Prestwick because on the whole the Scottish schools won't be on a half-term holiday at the end of May - they finish for the summer in late June and most will simply be off for the Jubilee weekend.
SM
