Yes they do, but you must understand a mess does influence how they feel about the property. It is the EA expectation that the house is fit to view. I wont say it affects valuation but just how confident the EA is about pushing the property forward for viewing.
We got our flat ready for sale by painting a couple of the rooms (£600), putting a new curtain rail and curtains in living room (£500)and sorting out a couple of annoying unfinished DIY jobs (£600). The biggest thing we did was to clear out the clutter and change the layout of some of the rooms to make them easier to see the potential.
These things made it easier to sell the flat, I don't believe it added any value to the flat. The big selling factor for us was location, location, location... If you are in the right area you will sell at the right place
3 bed with potential to be proper 4 bed, nought wrong with that. Can you do a comparison to see what 4 bed in the same road goes for?
The question by the sounds of it - is do you want to move? When doing your calculations don't forget to factor in stamp duty on your purchase, agents fees on your sale, moving costs, survey costs, fees for new mortgage. Would this swallow up some/all of your equity ?
If you have space, could you get a lodger to help pay the mortgage ?