I have never attacked the Brits openly but that hasn't stopped them before to make me the subject of an attack of opportunity.
Secondly Britains economy is in dire need of cotton (both America and I refuse to trade with GB ATM). GB might see the attack from the Ottomans as the perfect excuse to forcefully get there hands on some cotton.

So far the most cost/effective method I could find to defend my harbours and as much trade as possible would be the fortification (in depth) of at least 1 lane from the first harbour on the Nile up to the med.
I don't believe the Brits will actualy invade they're much to busy in the war with America but they can spare at least some of there navy (which would no doubt be stronger than mine).