The shape and normalisation of the β-delayed α spectrum from 11 Be was measured by implanting 11 Be ions in a segmented Si detector. The spectrum is found to be dominated by a well-known transition to the 3/2 + state at Ex = 9.87 MeV in 11 B. A significant increase in the observed decay strength towards the higher end of the Q β window means, however, that the 9.87 MeV state cannot alone be responsible for the transition. Using the R-matrix framework we find that the inclusion of an extra 3/2 + state at Ex = 11.49(10) MeV is required in order to obtain a satisfactory description of the spectrum. Both states show large widths towards α decay, exhausting significant fractions of the Wigner limit, a typical signature of α clusterisation. The observed Gamow-Teller strength indicate large overlaps between the two states and the ground state of 11 Be.