You're asking two questions. First, do moles store earthworms for later consumption, and second, can these "larders" contain 1000 or more earthworms?
There's little reason to doubt that moles keep larders. Here's a quote from Funmilayo (1979):
Moles are known to store earthworms which MacDougal (1942) suggested were caught during hard frost. Evans (1948) speculated that the earthworms in stores were caught while crawling in the mole's tunnels, but Skoczeń (1961) emphasised that earthworm stores were associated with winter nests and were collected during digging in mild spells in autumn and winter.
The article also looks at the composition of the earthworms stored by moles in their burrows. Not every fortress contained a storeroom:
Fortresses examined in March and October, 1968 and in March and May 1969 did not contain earthworm stores indicating that wild moles did not lay stores at these periods. All the fortresses (N = 5) examined in February 1969 contained earthworms with healed, decapited and mutilated bodies which indicated that the injuries were inflicted earlier on when the stores were laid, presumably after October, 1968 when last unsuccessful search was made.
The total number of earthworms found in these stores is given as 325, i.e. an average of 65 per store. This is far below the number cited in the Wikipedia article, but the sample size in Funmilayo (1979) is too small to draw any conclusions as to that number's plausibility.
I couldn't find any reference for Attenborough's claim of a store with more than 1000 earthworms. However, there are earlier reports that suggest stores of several hundreds of earthworms do exist. Here is a quote from Dahl (1891):
At the beginning of the next winter, on Nov. 27, 1887, Herr Schröter again examined two burrows without finding stores. The next spring, however, after a prolonged and severe frost, there were found on April 8, 1888, in one of the burrows examined—
578 Earthworms ;
67 larvae of Hepialus lupulinus , L. ;
4 Cockchafer grubs ; and
3 larvae of Skip-jack Beetles.
A second burrow which was examined at the same time was likewise filled with a number of worms. At the commencement of the third winter, on Dec. 23, 1888, after a short slight frost, there were again no stores found. But on March 12, 1889, after a severe and long-continued frost, we found in the first barrow 550 earthworms, and the rest of the burrows exposed also contained large food-stores.
Apparently, store size depends on the conditions: after prolonged winters with considerable frost are right, it seems that most burrows will contain large earthworm stores, and the reports suggest that it's easy to find some containing 500 and more specimens. Given these numbers, I have no doubt that a larder with more than 1000 earthworms is possible under the right conditions. All you need may be a particularly long winter and an environment particularly rich in earthworms inhabited by a particularly diligent and particularly toxic mole.
The store-keeping behavior of moles is well attested. I've found reports of stores containing almost 600 earthworms, and larger numbers seem fully plausible.