We present a detailed investigation into the recent star formation histories of 5,697 Luminous Red Galaxies (LRGs) based on the Hdelta (4101A) and [OII] (3727A) lines. LRGs are luminous (L>3L*), galaxies which have been selected to have photometric properties consistent with an old, passively evolving stellar population. For this study we utilise LRGs from the recently completed 2dF-SDSS LRG and QSO survey (2SLAQ). Equivalent widths of the Hdelta and [OII] lines are measured and used to define three spectral types, those with only strong Hdelta absorption (k+a), those with strong [OII] in emission (em) and those with both (em+a). All other LRGs are considered to have passive star formation histories. The vast majority of LRGs are found to be passive (~80 per cent), however significant numbers of k+a (2.7 per cent), em+a (1.2 per cent) and em LRGs (8.6 per cent) are identified. An investigation into the redshift dependence of the fractions is also performed. A sample of SDSS MAIN galaxies with colours and luminosities consistent with the 2SLAQ LRGs is selected to provide a low redshift comparison. While the em and em+a fractions are consistent with the low redshift SDSS sample, the fraction of k+a LRGs is found to increase significantly with redshift. This result is interpreted as an indication of an increasing amount of recent star formation activity in LRGs with redshift. By considering the expected life time of the k+a phase, the number of LRGs which will undergo a k+a phase can be estimated. A crude comparison of this estimate with the predictions from semi-analytic models of galaxy formation shows that the predicted level of k+a and em+a activity is not sufficient to reconcile the predicted mass growth for massive early-types in a hierarchical merging scenario. ; Comment: Accepted for publication in MNRAS, 13 pages, 10 figures