many of the best gardens in my opinion are National Trust, including the very special Hidcote and the very beautiful Stourhead.
Some guidance might be helpful to choose which to see, maybe that's why you want a guide.
I will say that almost all provide free intro tours of the gardens 2 or 3 times a day so if you can get to the gardens under your own steam you can do very well without a private guide.
There are gardens all over the country - which parts of the country will you be in, and which gardens do you refer to as "some of the major English gardens"?
By September some of the best displays will be heading over. Any chance you could move the trip up into June and July, when they are at their best?