Bare tiles, no lining below them...

[Blake1982]

I've just been into my loft to check out where the leak in my roof is coming from and if it was fixable without pro help, low and behold there is no felt lining under my tiles.

Checked where the leak is coming from and it is running off the next door neighbours felt that comes through on to my side. after closer inspection is looks like the person who lived here before me had removed it (as there are some pretty nasty jagged edges poking through) but never actually replaced it.

Whats the recommendation here then...?

 

[Deluks]

Loads of houses without felt, including mine. It's not really an issue apart from dust in the loft.
As for the leak, you should ask your neighbour to get his broke or missing tiles fixed. In the meantime you could somehow try and raise the edge of his felt so that the water stay on his side. Staple it or screw a vertical batten on to hold it in place.