OK...well, you will probably have Sacred Heart (catholic school) in there as well.
All those schools you have listed are great. If you are wanting to get into a church school because you are religious, then you probably stand an OK chance - if you are a regular church goer - because St.M&P, St.John and Sacred Heart reserve places for those with regular attendance. If you are wanting to get a place in a church school because you think they are better then you really need not worry. Both Hampton Wick and Collis are fantastic schools.
In the last few years, there has been a real clamour to get into Collis. It has a fantastic Ofsted report and really big grounds for the kids to run around in. It has a 3 class entry (so 90 in each year) and a 2 class nursery year (morning and afternoon, 24 in each class). It also has on site, for use in Summer, a small outdoor swimming pool. The teaching is brilliant and they have a lovely headmaster who is great with the kids. In terms of SATS (which I don't think are the be all and end all) it does very well and has managed in the last few years, to beat several church schools - something that a school which has no control over its entry other than siblings and distance is very good.
Hampton Wick is equally nice - it has a 2 form entry school with a nursery and lovely grounds. I think it's actual SATS are not as high as Collis (over the years) but don't let that put you off. Everyone we know who goes there, loves it.
St M&P is very well thought of and has a 2 class entry. We know a lot of people there and they enjoy it. It's hard to get into (as are the other church schools). Sacred Heart is probably the most difficult because they only take 30. All the church schools round here have religion as a main part of the schooling and have lots of services, lots of children go to Sunday school etc.
Here's the link to the council website (which shows you the website for the schools)
schools in Teddington, Hampton Wick
Most schools here are very happy to show you around so just give them a ring and see what you think.