Easy..as someone who has come in the opposite direction....OZ..to the UK, you need to be aware of the narrow minded and protection minded aviation industry that exists back home.
As has been stated before, airlines cling onto a requirement of 500-750 hours multi-engine PIC before you can even interview for a position on a transport category aircraft. Seems odd doesnt it?..but its the norm, they will look at your application...see that youve got x so many thousands of hours on a baby boeing, then dismiss your proffessional experience and skills because you dont have the required PIC time.
One other thing, dont expect an airline to help you with any immigration issues.
Id suggest you stay at the Big Orange, get your command, then attack your plan from a position of strength.
Cheers 757