well.... i believe if you engage your self in the expat scene in the city, you can pull off a nice job in one if the governmental related companies, or anything related to development in many fields.
my advice to you is to research the city a bit more, get to know what is missing, and what you believe you can offer better than what they have available, and i am sure u will find quite a few, and always network with people.
keep in mind that a lot of major companies, as well as Jordanian companies welcome hiring foreigners ESPECIALLY from the UK, due to the English language abilities, it can open a lot of doors for you as a foreigner from the UK.
hell.... you can even try to apply for a radio station commentator job, or even have ur own show if u have talking skills...
otherwise, i am not very familiar with your degree specialty, but that can only mean good...the more weird ur degree is, the better u can get chances there, especially if its in engineering, so i dont think u will have problems in that area as well...
as for applying online or sending c.V's, well i believe if you can just print our ur c.V and make some calls and try to secure appointments would be better...especially because u have the british accent thing going on, and that for Jordanian in specific indicated that you are well educated and useful for any business.... you can develop so many things by your self...even by doing consultancy jobs, and believe me, a lot of companies over there needs it.
so all u need is just present your self and ur strength points well... and everything else will take care of it self...
let me know if u need more details...
i'll be glad to help.
cheers