I am UK pport holder, i want to travel to Malaysia and the Singapore, Bangladesh & Thailand, do i need visa?

I am going to Malaysia for one month, from there i wish to visit other counties like Singapore, Bangladesh (have vis.a for this already in pport) and maybe Thailand. Will i have any visa issues or problems booking flight from Malaysia to travel to these other counties on my British pport? will i be okay to just book a flight on the internet from Malaysia to the other counties? will i have any issues getting back into Malaysia from the other counties? as i will be coming back to the UK from Malaysia