The correct expression is welsh rabbit. Rarebit was added by toffs who didn't want to be associated with cheap rabbit meat. Welsh was added to nouns to mean a cheap or poor version of something ie: using your fingers to straighten your hair was using a welsh comb. Cheese was seen as a poor substitute for meat (rabbit, or otherwise), hence the name welsh rabbit. On a similar idea, many people think lunch is an abbreviated form of luncheon. Again, this is wrong - toffs wanted to make boring old lunch sound posher and created the ridiculous luncheon.