BBC News reports that the recorders are being sent to a European agency for processing and analysis (presumably either the French BEA or UK AAIB). It also stated that the AAIB had been accredited to the investigation, so they may well go to Farnborough.
The NTSB, as a party to the investigation, had (not unreasonably) been pressing for the recorders to go to the USA, but despite their fierce independence from the FAA, it would seem that the latter's decision to allow continued operation of the Max in the USA (not to mention Trump's comments) may have had a bearing on the decision.