Most Trans-Atlantic cruises are in the spring and fall, as cruise lines reposition ships between Europe and the Caribbean. Looks like your only option in June or July is (see below) the QE2...New York has the most flexible flights to the UK, from its three major airports.
June 2012
June 10th: 7-day cruise from Southampton to New York on the Queen Mary 2 June 24th: 7-day cruise from Southampton to New York on the Queen Mary 2
July 2012
July 27th: 7-day cruise from Southampton to New York on the Queen Mary 2
June 2012
June 10th: 7-day cruise from Southampton to New York on the Queen Mary 2 June 24th: 7-day cruise from Southampton to New York on the Queen Mary 2
July 2012
July 27th: 7-day cruise from Southampton to New York on the Queen Mary 2