If you go for the lastminute.com £10 child's full annual pass, you do need to book it and turn up for a date before the end of May, but all you need to do is take your lastminute.com printout to the guest services window and exchange it for a printed ticket. Then the child in question exchanges that ticket for the pass when they come to the park (and that part can take place after the start of June, if I understood the way it was explained to me today correctly). So if you live within a not-ridiculous drive from Legoland it may be worth doing.
There's a rumour they may be doing a similar offer on adult annual passes in June.
Also, an annual pass holder can bring a guest for half price on Thursdays.