Flying around the world is really a journey without end, rather set yourself a target in some far off land and make that the journey of a lifetime.
From your location in Blighty a reasonable destination would be Sydney Australia, you won't have to fly over Russia and you may be able to find a way round Egypt.
I am not familiar with GA in the Middle East but it does exist in India and in all countries to the East e.g. Myanmar, Thailand, Malaysia, Indonesia and of course Oz.
As mentioned by
IO540 logistics is the key, Avgas can be made available wherever you need it and flight clearances just require a bit of patience.
Our club in Kuala Lumpur has brought in 2 Cessna 172 from the East Coast of Australia, no big deal, about 4,000nms across the island of Oz, crossing the Timur Sea to Indonesia, stopping off in Bali for some R&R and then via Java and Sumatra into Malaysia.
Similarly trips from here through Thailand to Myanmar have been undertaken.
You could start by contacting Flying Clubs in the countries you plan to fly through, nothing like local knowledge to help you on your way.
My 2 dollars worth
