When does the english schools finish for summer?
Term 3 begins in early April or mid April and finishes mid May with a week half term. It resumes in late May and finishes in mid or late July. 
When does the english state schools finish summer term and holiday begins?
end of July late July second week of July
English school holidays
No context provided
When does the english schools on Trinity term finish for summer?
ends on and includes 6 July about the end of June
English school holidays
https://en.wikipedia.org/wiki/English%20school%20holidays
Academic term
https://en.wikipedia.org/wiki/Academic%20term
The English school year runs from early September to mid or late July of the following year. 
English school holidays
The summer holiday begins in late July and is usually about six weeks long, sometimes ending only two weeks away from the Autumnal equinox.
English school holidays
Term 3 begins in mid to late April and finishes in late May with a week half term. It resumes in early June and usually finishes during mid to late July.
English school holidays
Trinity term is the third and final term of the academic year at the University of Oxford,[1][2] the University of Dublin,[3] Canterbury Christ Church University, and some independent schools in the United Kingdom. It runs from about mid-April to about the end of June and is named after Trinity Sunday, which falls eight weeks after Easter, in May or June.
Trinity term
In the English school system, state schools run from early September to mid or late July of the following year. The summer term (also known as the third term) runs from late April and finishes mid to late July with a week-long half term break in between. The summer holiday begins in late July and usually runs about six weeks long, ending in September. The schools on the Trinity terms end their school year and begin summer holidays a few weeks earlier, at the end of June.