Originally Posted by SirRagnar

Yes the routing is the challenging. I can't really make that call for you and I haven't looked up the time schedules of the various flights.
I suggest you look up time schedules first and then plan the route accordingly.
If you can end up in LCY rather than LHR you have just saved yourself 1-1½ hours, since LHR is far out of city and immigration lines are horrible (The UK is not part of Schengen, which allows you to travel without immigration).

If you want to start in BCN then Spanair flies direct from TLV to BCN and from there you can go to BRU with Spanair as well. Spanair is decent, but nothing spectacular (no European airlines really are). They will have cava in the lounges though
From BRU you can then cover AMS by train and jump to London (unfortunately not to LCY though).

Let us know what route that you come up with