The 3' beds sound about right Steve, but I think that you will be a bit cramped with only 1' between them. I would go for 2' for comfort. And, remember, that the wall of the beds will have a thickness! If you are using boards then the thickness will be minimal but if you are building with wooden beams then it has to be taken into consideration.
The lady next door got her bf to build raised beds. He used 5"x10" beams, 2 high! A little bit OTT, I think.

In addition they are too wide so she has to walk on them thus defeating the objective of a raised bed!

I will be using some old fence palings that I have been given and also one bed on another part of the allotment that will be used for carrots I will be using some old scaffold planks and will be about 18/20 inch deep and filled with some free top soil that’s available on the site.

Sounds good Steve - look forward to the blog!

If you will be using a wheelbarrow - for compost etc! I would make the paths between the beds the width of your barrow's legs. It will make life easier in the long run. Three to four foot is a good width for the beds - as you need to be able to weed/plant in them without stepping on them - how long are your arms?! Also if they are 20ft long - you will always want to get to a fork or something when its on the other side - think about how far around you will have to trot to get it! Perhaps two 8ft beds would be better. And look at the direction the site faces, the best (most light) way to orient the beds is lengthways north to south, then whatever the crop (important to rotate crops each year) they will get enough sun.
Deep beds are great tho' - you can plant closer together and garden in inclement weather - and since that's all we've had this year, its definitely the way to go!

I would make them 4 foot wide.