Randstad are massive in all sorts of sectors. I used them a few times to recruit for specialist IT roles which we couldnt fill directly. They were OK; pricey but actually delivered decent candidates. Whether I would want to use them exclusively to staff and organise a national tutoring programme is another matterRandstad are massive in teacher recruitment. Have been for years.
Not sure who exactly has the best track record in this type of pupil catch-up program, but surely a decent start is a large company, working across international boundaries, who work heavily in the education sector.