Answer supplied by Ivan Valtchanov:

The SPIRE beams for both the Photometer and Spectrometer are available as ancillary data products (ADP) in the Herschel Legacy Area:

http://archives.esac.esa.int/hsa/legacy/ADP/PSF/SPIRE

For the SPIRE Spectrometer in sub-folder SPIRE-S and in subfolder SPIRE-P for the Photometer.

The SPIRE beams are also are available within the calibration tree and can be accessed using the Herschel Interactive Processing Environment.

You can also obtain the Photometer beam data by going to the release note:

http://archives.esac.esa.int/hsa/legacy/ADP/PSF/SPIRE/SPIRE-P/README.html

For the spectrometer, the release not is here:

http://archives.esac.esa.int/hsa/legacy/ADP/PSF/SPIRE/SPIRE-S/README.html