Alcohol is a prominent aspect of the milieu that surrounds Neddy Merrill. As the story opens, impressionistic bits of dialogue suggest that everyone, from the parish priest, to the leader of the local bird watching group, to Neddy's hosts (the Westerhazys) drinks to excess at least sometimes. Moreover, when Neddy conceives of his plan to "swim home" via a "river" of suburban swimming pools, he has been drinking a "glass of gin" at the pool with his wife and the Westerhazys.
At many of the suburban homes he visits along the way, the people and their guests are socializing and drinking. It is part of the landscape of how they live their lives. What becomes apparent by the end is that Neddy has somehow lost his home and great swaths of his memory. Teddy's thought processes and experiences in the story suggests a binge-drinking episode and periods of blackout. Neddy's alcoholic confusion doesn't seem to stand out very prominently, however, suggesting that being drunk, to at least a certain extent, is not unusual for the people that Neddy moves among.
In The Swimmer society is presented as an on-going "get together" in which alcohol is always present. In the case of Neddy, we know that he was going downhill in debt, in his professional life, and in his family life. However, the story does not present it right away. Yet, we see that Neddy is indeed an alcoholic and uses alcohol to wash away his reality. As his illness progresses, and his obsession with swimming across the county becomes stronger, he would become more impertinent by crashing yard parties, getting heavily intoxicated, and moving on. In one of such "crashings", he finds out that alcoholism had nearly taken the life of a fellow peer, Eric Sachs. He could not remember this.
Hence, it is clear that alcohol is a self-medicated solution to the collective problem that seemed to be going around men like Neddy: They could not keep up with appearances and used alcohol to escape. In Ned's case alcohol aggravated his already-created condition, which came in turn as a result of him having lost everything.