I assume that Redbridge is your home LEA, so you already know that the entrance test for the Redbridge grammar schools (the boys' and the girls', Woodford County) is set by the Centre for Evaluation and Monitoring (CEM), part of Durham University. The same exam is used on the same day in September for several other areas - all this is on the Redbridge website. Pupils can register to be assessed for eligibility for any of the schools using the same exam (obviously depends on gender), but only sit the exam once.
CEM do not produce any practice material, other than a short familiarisation paper - which you will find on the Redbridge website - nor do they actually endorse any of the myriad 'CEM' material sold by other publishers.
(Already, this year, someone has posted that
the real exam their child sat didn't have anything in it that they had found in the 'CEM' books that they had bought
'Near' to Redbridge, you have Latymer (which uses the same exam but I think gap some kind of 'maximum travel time' catchment?) and KEGS in Chelmsford (Consortium of Selective Schools in Essex exam). Queen Elizabeth Grammar School in Barnet (own entrance exam) has no catchment and is regarded as 'near' to most of Greater London, it seems, and Colchester Royal Grammar School (no catchment, CSSE exam) is also regarded as a local school for Redbridge, if posters on the forum are to be believed, although there are some of us who would consider that a ninety-odd round trip rather precludes that. I went to a school which was predominantly boarding and some of the boarders lived a lot closer than that, but as I've said before, we each have our own parenting style.
No idea about QE, but you can find free familiarisation papers and an order form for some past papers on the CSSE website; the exam format is one English (with a bit of VR and a continuous writing section) paper and one Maths (with a bit of NVR) paper.