For Woodford County High, it would be more of a case of just being able to pass the 11+ - more like being in the top 0.5%. There are at least 10 x applicants as places, and most would be from kids above 11+ standard.
The three privates mentioned are all excellent. Forest could be a problem travelling by car, as you would be going in the sane direction of City commuting traffic. All three have 7+ entry (I believe Forest start at 4 also) with around 4x applicants as places. This is higher at 11, although more would be making a higher number of applications as more choice at 11. Of the three, Bancrofts is definitely the most academic. Chigwell are excellent on music and sport, as well as being good all round academically. I have also heard that there are higher numbers of students getting into medicine from Forest due to connections - not sure how true this is.
If your sister is interested in independent, then it could be worth enquiring about starting in the juniors - some will have places come up in yr5 through kids leaving. Is there any reason she wants your neoce to stay at current primary?
Quite a few Epping Forest parents send there kids to St.Edmunds in Ware, Herts. Quite a few that don't make the grade for the 3 above. Although down as a Catholic school, it is not only catholic intake. Ther is also a school bus, that hoes through Loughton and Buckhurst Hill AFAIK - not sure about Chigwell.
The only state comp in Chigwell itself is West Hatch. Although in Epping Forest, it Borders Redbridge, so the intake is from both. It is generally up to a mile straight line distance. Siblings are higher priority, regardless of distance, so "catchment" will vary. So this mainly covers Chigwell, Hainault, parts of Buckhurst Hill and Woodford.
Davenant is in Loughton, but there needs to be ~7 years of church/synagogue attendance proved.
There is also Roding Valley in Loughton which mainly takes kids from Loughton and Buckhurst Hill. Averagish on the league tables, recently changed head which I have heard has been an improvement.
Both West Hatch and Roding Valley are generally heavily oversubscribed. For 2010 WH 724 app for 189 places, RV 586 fir 240 places. This is straight from the admissions booklet.
There is also Debden Park in Loughton, which was under special measures a few years ago, but appears to be on the up. 357 app for 180 places in 2010.
King Harold School in Waltham Abbey is the one most Epping Forest parents appear to be avoiding - 145 app for 220 places in 2010.
There are also v.good Grammars further out in Essex, which should be less competitive than Woodford as there are more of them. Not sure how feasible the commute would be though.