I think Lee's reference is well explained by a quotation of George Bernard Shaw's cockney flower seller Eliza Doolittle. From memory it's something like this: "In 'ertford, 'ereford and 'ampshire 'urricanes 'ardly hever 'appen."
And bodgyuk's laundry fetish reference is truly apt. Aren't we all interested in pee-stained briefs and boxer shorts from the laundry??
OK, the pun or witticism is that OMO is a brand of laundry detergent (where is that registered trade mark symbol when you need one?), ergo omo-sexual must mean someone who gets turned on by laundry washing or detergent.
Traditionally a Cockney is someone who is born within the sound of the bells of St Mary Le Bow church - a large swathe of the east end area of London.