i don't think this is canker,this could be due to the weather conditions,lack of water and things like that,but i'm sure others will be able to help,if it has only affected the smaller branches they can be pruned out,but i would wait awhile to see if it spreads abit more and if the leaves appear ok first before cutting bits off.

My apple tree also suffers a little from this so I'll be interested to see what is suggested! I generally prune these bits off.

Thanks for your answer, it's just that last year's apples were marked with scab and the leaves were also marked.
I was told that this particular variety of apple tree is prone to canker.

yes you are right,worcester pearmain does have a problem sometimes with scab and canker,i'm not a lover of spraying if i can help it but rake up the leaves and burn them if your tree has had bad scab,again the weather can make scab worse,i would still wait awhile,before hard pruning but i would give it a feed to boast it up.

I have now added another image to my question above showing a typical piece of disease wood, which I pruned off the tree this morning.

oh not looking good.this could well be canker.
i think i would cut out the branches and paint with arbrex,you may well lose all the fruit as you know this tree is a tip bearer but it might save it in the long run.