Sam,
Under WP rules you can work in supplementary employment i.e. in same field but with different employer and as a second job (as opposed to it being the main one) without needing a WP. The issue here is the 'similarity' in material taught in Sec schol vs FE College - if its say GCSE's, GCE's in both institutions then you are o.k.
Accordingly there is no need for fresh FLR - the one you have should suffice subject to it being valid and the secondary school employment continuing when you re-enter the UK. Make sure taxes and NI contributions are deducted as relevant for both jobs. You can send me half the WP fee and the FLR fee for my advice

- actually splash it on the missis..am sure she deserves it. Have a good holiday.
PS - I have deleted your duplicate Q