First you need to be sure from a safety point of view.
Is this a personal recommendation - does he currently teach at a school?
If not then you need to get some references!
CRB check is a tricky one but I would never be out of earshot/ door open etc anyway.
As to teaching I would say that an English degree is no guarantee & few primary school teachers will have one!
More important to find out what experience he has in tutoring & what his approach is.
I would hold back on telling him too much about your child & get him to do an assessment & see if what he says shows understanding of their strengths & weaknesses. Not that he can be expected to figure out everything in one session! but you need to be on the same wavelength.
Its then a case of giving it a go & see how the two of them get on - different tutors can work with different children (just like in school) and with a young child they do need to enjoy the sessions.
If you find a good tutor then the child's confidence should show signs of improvement pretty quickly - and hopefully 'performance' will follow
Hope it goes well!