I was using window functions, and this appeared to work, but it's a small sample size, so perhaps there's a flaw here:

SELECT t.*

FROM ( SELECT top 10

id

, start

, 'prev id' = LEAD(id) OVER (PARTITION BY p1 ORDER BY updatedate)

, 'prev start' = LEAD(enddate) OVER (PARTITION BY p1 ORDER BY updatedate)

, updatedate

FROM #test AS t

ORDER BY updatedate desc) a

INNER JOIN #test t ON t.id IN (a.id, a.[prev id])

WHERE a.updatedate > '20150701'

AND a.updatedate < '20150720'

Some extra columns in there, just to show what's happening.