Personally I think Paweł's story isn't adding up and he is denying he went into Oak road Playing Fields that night with Libby, so the police are looking for any evidence that they entered the park. The CCTV likely indicates they drove somewhere very close to this area, and the screams the neighbours heard indicate something might have happened to a girl in the park. The police could have CCTV footage of Paweł returning home after these screams were purported to have occurred. Its far too much of a coincidence.
There's a few things that spring to mind. Paweł may smoke a particular type of cigarette/tobacco and his dna (possibly shared with Libby if she took a drag) could be found. Paweł was stealing condoms from the students houses, and he may have used one in order to not get arrested later for rape. A condom could have been left behind and would have both their DNA on it. Finding anything belonging to either of them could narrow down the search area because it would indicate whereabouts in the park the incident happened.
If there was a scuffle, which it sounds like there was, personal items of Libby could be scattered somewhere. We know she didn't have her phone, and possibly not her keys, but she probably had her wallet (which she used to pay for the taxi home) and obviously her clothing which they have an accurate description of, and if there was a sexual intention her underwear could have been removed and shoes fallen off. One thing I find silly on behalf of the police is that they seem to have not sealed the area. The damp mud could have preserved perfect footprints, and Libby was wearing Vans old skool shoes, which I also wear, and they always leave a distinct mark in the mud because they were originally designed to grip skateboards.