I am a software developer and now have the option of working anywhere with a laptop and internet connection for a UK company, so seeing some of the world seems like a good idea, my job can keep me financially sorted for my trip.

Will I need a "work permit" for the countries I visit? Since both the job and company are located within the UK.

I don't know what countries you plan to do this in but if you do it in Thailand it is not likely to be a problem; unless you are found out. Work without a work permit is not allowed.

In your situation you can enter Thailand as a tourist, with a Tourist Visa, which gives you 2 months with a further month of extension possible.

A double entry tourist visa would allow you almost 6 months stay, with a brief trip out and in, in the middle.

If you use your computer to connect to the internet it is very unlikely anyone will comment,

unless you bring it to their attention that you are working........