TGG to SIN via KUL (Need to collect bags @ KUL?)

Am booked on single BA PNR from TGG to LHR via KUL then SIN. MMB on the MH shows it as a booking from TGG to LHR..

Am I right to assume our bags will be checked through to LHR and we'll get boarding passes for all flights?

Ask as I note from the KLIA website that we should pass thru Immigration & Customs at KLIA before the leg to SIN...

... and am hoping we won't need to collect our bags @ KUL and then re-check-in

Thanks