I'm in the same boat. Rather than doing LHR-BAH, why not LHR-DOH (Qatar)? It's the same BA plane which stops in Bahrain, but, despite being further from LHR, is much cheaper for starting another RTW and gives you more mileage.

As they're both in RTW "Europe" you can change your existing CAI to DOH for a change fee without re-issuing the ticket or paying a fare increase as long as you have already flown the first internatonal sector on the ticket, which you clearly have.