We bought a 1930's house 18 months ago and it was suggested that the roof could have a few- 10 years left.
From the ground it looked fine, even one of the roofers doubted it, however the tiles were like biscuits and very worn.
We had no leaks 
Anyway we got three quotes two about 22k and one for 32k
We have just had it finished and it looks lush
Both chimneys were re-pointed
Our leading was redone around chimneys and bay
The bay, when everything was removed, showed signs of water damage.
Anyway, my point is the decision is yours.
It may be ok, it may not.
We decided that ours had lasted 100 years, more or less, but we knew it would need reparations in time.
I did not want a leak or tile slippage or something else chimney related.
We took a punt and it has been done
It is up to you really 