a) The
carriage of an ADF is mandatory for IFR in controlled airspace in the UK.
b) The
carriage of a DME is mandatory for IFR in practically all of Europe.
There are no known prosecutions in the UK, on the above - despite much rumour on pilot forums
As bookworm suggests, even if a) is removed, a plane without an ADF will still be practically useless for IFR, due to the large number of approaches in UK and abroad which feature an NDB.
This leads to an interesting debate whether an ADF should be
used for flying these; suprisingly there appears to be no legal requirements for that. I think most smart pilots fly NDB approaches using their GPS (either using the OBS mode, or using the overlay) while checking the ADF at the top of descent.