Will the 5 speed type 9 gearbox fit onto a 1300cc 4 speed engine and what is involved in its fitting?

A little sketchy on the information there, but assuming it's a 1300 crossflow and you had an Escort Type E or similar then the clutch plate you have is a 7/8" 20 spline, the 5 speed is a 1" 23 spline.
Type 9 has same bell housing pattern so should bolt straight on.
Type 9 5 speed is longer and has different output splines so prop shaft will need changing.
Type 9 mount is further back than the 4 speed.
If you had a 4 speed Type 9 then it's the gearbox mount and shorter prop only.

There are many different Ford 4 speed boxes, 4 are pretty common fitments in kit cars. Oldest is what is commonly called the 2000E box. If its ones of those you will need a new prop, clutch, gearstick, bellhousing, mount and speedo cable. The next is the type 3 box (a single rail version of the 2000E). This is probably the most common as it was fitted to 1300 and 1600 Cortina's, Capri's and Sierra's for many years. Parts needed as 2000E. Next is the Type E, very common again since it was fitted to all Mk1 and Mk2 Escorts with the exception of the RS versions, parts list same again. The last one is the Type E (sometimes called Rocket) which many people refer to as the 4 speed type 9 since the latter was loosely based on it. This is the easiest convertion since you will only need a gearstick, mount and longer speedo cable, know this because I did the conversion some years ago.

Paul