Will I be able to travel freely and have a good time with a budget of £2000 over two months, or will i end up missing out and wishing I had saved up more?

Things like (multi day) jungle tours and kayak tours are not that cheap. The visa for Laos, Cambodia and Vietnam are also not cheap, same with the required medical vaccinations against tropical diseases. And what about the flights? Does that £2000 include the flights? And travel insurance?
Taking the bus in for example Laos is cheap but how to get to the bus station? These bus stations are often far out of town and often require a tuktuk ride to get there. It adds up.

If it doesn't include flights but is just for spending once in SEA, , we have managed on a similar amount as a couple.
remember the moreyu move, th you'll spend.eo

It also depends on what you consider a good time, many things are quite cheap but beer etc. is not and a lot of people spend more on beer than everything else.

Having a good time is indeed subjective, I met an America girl in Laos who had travelled by normal bus (without a toilet) from Vang Vieng to the 4000 island area, it was a 26 hours ride or so. I don't do that but it saves one night of accommodation. Night train is okay for me but not the night bus.
Also visiting the night market and trying everything can become 'expensive'.
ATM fees were a biggie during my last trip to Thailand and Laos. Maybe there is a way to avoid those?
As above..it depends.If you are not including flights,and if you live like a 'backpacker'...not luxury,not 5 star hotels...and IF you don't spend a lot on drinking,nightlife and tours...you can do it quite easily.
Beer is cheap in SEA but of course like anywhere you can pay through the nose at some places.
How much you need really depends on YOU and where you stay, eat and drink and then of course there are places (Angkor Wat) or activities that will blow a big hole in your daily budget
Help yourself by telling us more about your aspirations and we might be able to get closer to giving you an answer
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