Depending on the cloud base and if you do not need to go down to an IAP MDH/MDA equivalent, you could let down to 1,500ft on e.g. the 120 radial from BNN. NB - this is not an instrument approach to Elstree but just a way of getting below cloud.
I'm not sure how easy it would be to use the Northolt ILS inside the London CTR for this? Cranfield and Oxford (or even Luton, but same comment re. CAS) are also alternatives.
But, ultimately, if the cloudbase is forecast/reported to be below 1,500 (or possibly 1,000 if you feel courageous), you should probably not be trying to get into Elstree that day...
As an aside, even with an IAP and full ILS, airfields may be below weather minima - assuming you do not have a CatII or III equipped aircraft :-)
B.