Lambeth were in crisis a few years ago, and have actually, as far as I can see, acted quite effectively since then - a brand new two-form entry primary is opening near us in September, on the site of a well-regarded secondary, to be an 'all through school'. Meanwhile another local primary is having a new building and is part of a federation which is increasing the number of places. They have opened 2 secondaries (that I know of - Elmgreen and Evelyn Grace) ) in the last 6 years, and have another opening in September.
But as NotCitrus says, the new places may soon be taken up.
The standard of education in Lambeth schools has been rising, I think it was one of the boroughs recently revealed as a place where you had the highest chance of your child being in an 'Outstanding' school. Certainly the ones near us are excellent and very popular. But this, coupled with the financial cllimate, has stemmed the flow of children into private schools and put more pressure on places.
In neighbouring Southwark the Free School phenomenum is resulting in no less than TWO bi-lingual English / German primaries opening not far over the border from us...so all fine there as long as you are happy to choose between faith or bilingual German. No particular reason for the German except that that is the interest and expertise of the guy who started it, and they believe that bilingual edcuation per se is a good thing. With which I agree, but wouldn't have chosen German. Such is the random nature of Free Schools. That is in an area of schools shortages , too.
There is high immigration and migration in Lambeth, but very little employment. I wonder how many recent EU migrants will stay long term in Lambeth. House prices and rentals are rising, and in short supply.