DD is exactly the same - both writing and at home, you could be describing her down to a tee. (She's also very slow at sports - always trails in ages after the last one in any race etc. despite being keen and really quite fit)
She's 10 this month, and in yr 5. We've plugged away over the years with school - partly because looking a few years a head the slow writing is obviously a problem for the future in terms of exams, coursework etc. But also its an immediate problem in that she is always being kept in at playtimes to finish work, in trouble for not getting things done etc etc, and this had reached a point where she was becoming very unwilling to go to school.
She's finally been referred to the Educational Psychologist, and (after a false start as the normal Ed Psych became long term sick) has just had her first assessment.
We weren't wildly optimistic beforehand, but we were really impressed - the EP asked to see us as well as dd, has given lots of helpful suggestions already (including working on keyboard skills as a fallback position), and is going to see dd further at the end of term for further assessment.
If nothing else she has I think made the point to school (fairly forcibly, seeing the letters that she's copied to us) that (a) it isn't simply dd being stubborn and refusing to write - which basically every teacher thinks is the case for at least the first term of having her in their class and that (b) if you put dd under time pressure she panics and gets even less able to put anything on paper.
I guess my main thought at your point (in yr 3) would be to keep in touch with school, ask what they're doing to address the problem, and really be aware of what is going on. Does his teacher think that it is a bad enough issue to involve the SENCO?
TBH that wasn't massively helpful for dd - its a very small school and the SENCO is the headteacher, who is also head of another school as well. But I guess the thing is that if your ds does have a longstanding problem you want to be moving down the road to getting some kind of intervention.
Oh, and one final thought - dd eternally had the same target set for her 'finish work in the time set' - date eg "by end Jan 2012" and we made a point of speaking to the teacher each time she had reached the target date "I just wanted to check in, dd has this target set, we're now at the end of January, it doesn't appear that she is making any progress towards it, what happens next?"