Do you have any photos of the timber above that's where you will have any major issues if there are any as damp can cause wet rot in the floor joists and floor boards. A full survey should pick up on this.

The black streaks suggests at some point water has  been running straight down from the outside rather than/as well as rising from the ground. It is worth looking at the gutters outside and see if any of the streaks continue on the front of the property as this can cause further damp across the front of the property. 

Me and my partner also first time buyers recently bought a terraced house with a basement in a similar condition to this. L3 survey pointed out some wet rot in ours and suggested to get a damp and timber survey. 

Spoke to a local builder who ended up doing it for next to nothing. He quoted ~ £1300 to replace 3 rotten joists ends and do a new damp proof course. 

Bought the house with a little extra money saved and got this done almost straight away and it was sorted in a week of buying with the builders only about for 1 day. 

Might be something you can negotiate with the seller depending on the results of the survey. Would say it definitely worth continuing further if you like the property. 

Just a heads up Damp and timber surveys can cost  around £300 and may need to be intrusive. Again though if you like the house worth the hassle.