The Luton and Essex controllers rarely have the time to solve this little problem for you. (Bourn is about 7 miniutes from Class D and about 8-10 minutes from the usual Class A entry points). This time is not enough to call London Info to request and obtain a clearance without orbiting outside CAS for an uncertain time.
I think that is the nub of the issue. My examples above made the assumption that the intention was to depart IFR into the airways system, because simply getting an IFR clearance into class D is not a particularly onerous task.
The workload associated with negotiating your own clearance is not trivial and can involve you flying, if not orbitting outside controlled airspace for some time. This makes the UK somewhat unique in requiring IFR pilots to carry VFR charts with them - just in case. UK-based pilots may cope with this adequately. There are many horror stories of foreign pilots struggling badly when their "clearance" contains the line "remain outside controlled airspace". Hard in a C182, very hard in a Citation.
It is a pity that the airspace is too busy and too "uniquely" designed to permit the widespread use of US-style "void after" telephone IFR clearances.
2D