'Leave xxx heading xxx' implies that you will hit the point on the required heading - not pick it up after the point.i.e you manoeuvre before the fix to be in a position to be on the desired heading as you pass over the point.
As 055166K states - if someone said 'After xxx, fly heading xxx", then you initiate the turn as you pass over the point... is you are high and fast then that will mean a bigger radius of turn.
Unlike 0055166K, I work at Swanwick on the TC side (LTMA) - the technique in our work is very relevant as it only involves about a 20 or 30 degree heading change and is applied primarily to aircraft on SIDS in a bid to position them between two stacks to enable climb.
It could be a rather poor technique to employ at higher levels, especially in regions where there are a lot of airways packed into a small space.
The phrase "after xxx fly heading xxx" is much less ambiguous and ope to interpretation than "leave xxx heading" - though to a native English speaker, both should be self explanatory. Unfortunately we get a lot of ATCOs nowadays who have never flown and have a lack of experience of aspects of aviation other than the specific type of controlling they do... they are the ones who need educated as to what the difference is between the two phrases.
If in doubt - safer to ask (though it may cause even more confusion due to the factors in my sentence above)!