That sort code applies to the 'Nottingham group' of Barclays branches. (i.e. several local branches share a common sort code). The 'head office' of the local group is almost certainly the main branch in the centre of Nottingham:
Barclays Bank plc,
2 High Street,
Nottingham NG1 2EN
There are several postal addresses (with various postcodes) associated with that sort code, representing the different branches within the local group. As stated, I believe that the 'Branch Manager' (who actually looks after several branches in the area) is most likely to be based in the High Street, Nottingham branch. However, mail addressed to any of the branches should still reach him, so JD's answer is just as valid as mine.