Any towered (ATC) airfield should be able to make the phone call to London Control and get an IFR departure for you before you get airborne. They won't get you an IFR clearance as such but they will get you a squawk and a contact frequency, so when you get airborne and call up London Control with your tail number they will know all about you and give you vectors/levels etc right away.
Otherwise, as mm_flynn says, it's a case of calling up London Info and asking them to do it.
I have never heard of an officially authorised way for you to contact London Control directly before getting airborne.