I agree with what the article says, but They don't mention about how thousands have turned their front gardens into places to park their cars, which doesn't help things either. So much is being paved over.
"There are three ecological functional groups: epigeic earthworms break down surface crop residues and their presence is linked to the breeding season success rates of the song thrush (Turdus philomelos), the latter whose populations have rapidly declined in England."
This doesn't actually say that the loss of earthworms are the cause of long term decline in Song Thrushes, only that access to a type of earthworm in the breeding season is critical for that breeding season's success, something which is always going to be affected by annual weather patterns, particularly long dry spells. Without historic data on epigeic earthworm numbers it isn't possible to say that epigeic earthworms are in decline on arable land so while it is obviously true that a decline in the availability of the worms year on year would impact Song Thrush numbers, it would only be speculation that this was the case. The quote  comes from this study onlinelibrary.wiley.com/doi/abs/10.1046/j.1474-919X.2003.00202.x
"Summer diet and body condition were compared in two farmland Song Thrush Turdus philomelos populations in south‐east England. One population on mixed farmland was stable and the other on arable farmland was rapidly declining. Summer diet was dominated by earthworms, snails, beetles and insect larvae (mainly Coleoptera and Lepidoptera). In both populations there was a pronounced seasonal decline in the quality of the diet, with preferred earthworms dominating prey items during March–April and snails dominating during June and July. Dry weather during late summer was associated with reduced proportions of earthworms and snails, and increased proportions of spiders in the diet, and dry soil conditions had a weak negative influence on the body weights of chicks (in the arable population) and adults. Despite a tendency for earthworms to constitute a higher proportion of the diet in the stable population, and for snails to constitute a higher proportion of the diet in the declining population, the body condition of chicks and adults appeared to be unrelated to diet composition and did not differ between study populations. Changes in agricultural practices have probably caused a major reduction in the availability of key summer food resources for Song Thrushes on lowland farmland, and we speculate that breeding thrushes mitigate the impacts of food shortage on chicks by confining their nesting attempts to localities and periods where invertebrate food resources are adequate to raise a brood of young."
That points to where a cause of Song Thrush decline may lie but it doesn't seem join the dots as regards to earthworms with certainty and is perhaps only part of the picture with reductions in moth and butterfly larvae also being an important element in reduced breeding success, which may in turn be related to loss of habitat - hedges, woodland etc and reduced larval food plant numbers.
"We review current knowledge of demographic mechanisms and environmental factors implicated in the population decline of Song Thrushes Turdus philomelos in rural Britain since the mid-1970s, and present new analyses of regional variation in population changes. Increased mortality during the first year of life (from fledging to recruitment) is highlighted as a potential demographic mechanism having driven the population decline, while Song Thrushes in a rapidly declining farmland population were making too few nesting attempts to sustain local numbers. Breeding Song Thrushes are strongly associated with non-cropped habitats such as woodland edge, field boundaries, gardens and scrub; they make substantial use of grassland, but avoid cereals when foraging. Earthworms constitute a key component of Song Thrush diet and the availability of this prey is strongly influenced by moisture levels in surface soils. Several lines of evidence suggest that dry surface soils during summer are deleterious to the productivity and survival of Song Thrushes, and regional variation in the rates of population change in Britain during 1970–86 was negatively correlated with the extent of under-field drainage on farmland (the main function of which is to promote the drying of surface soils). Increasing dryness of agricultural soils and the loss of grassland from eastern arable counties have probably both contributed to the declines of rural Song Thrushes in Britain. Loss of hedgerows and scrub, and the degradation of woodland may also have contributed to population declines but the role of predators remains unclear. Recovery of rural Song Thrush populations requires challenging new policy initiatives that should aim to restore nesting cover (scrub and woodland understorey), grazed grassland in arable-dominated areas and damper soils in summer."