The AAIB responded quite quickly (and briefly) but were not very helpful:
AAIB does not release FDR raw data on any accidents in line with
the EU regulation 996/2010 article 14.
Having a look at the corresponding EU regulation:
The safety investigation of accidents and incidents should be
conducted by or under the control of an independent safety
investigation authority in order to avoid any conflict of interest and
any possible external interference in the determination of the causes
of the occurrences being investigated.
Paraphrased, I don't think they want 'unexperienced' people interpreting data on their own and making conspiracy theories or something I guess :) That being said, the regulation doesn't expressly forbid the distribution of information in my opinion, but I won't bother discussing it further. I think that unless you have a proper reason for it, they won't give it to you.
Update: Paragraph 35 is interesting....
The rules on access to data, data processing and the protection of
individuals laid down in relevant legal acts of the Union should be
fully respected in the application of this Regulation.
which may imply that you could get it, depending on how those are written, which I have absolutely no clue about.