Extracting cell-free DNA
To note: I have no personal experience with this protocol. I am forwarding this paper, passed on to me by a colleague

There are many kits and methods available that don't rely on Qiagen. Or alternatively, if you ask them nicely, they do heavily discount their first kit you buy off them as a sort of trial (as they dont do samples).

However, to answer your primary question, are you adding a detergent and heat denaturing your samples first before phenol-chloroform (Triton/Heat/
Phenol)?


  Blood samples for CFDNA
  analysis are collected into EDTA tubes and held at/or below RT
  (18 °C–22 °C) for no more than 2 h before separation of plasma.
  Plasma should be separated from whole blood samples by double
  centrifugation (800 g and 1600 g for 10 min, separately), avoiding
  leukocyte lysis. We prefer to isolate CFDNA immediately after plasma
  separation to minimize the effect of prolonged storage. Otherwise,
  samples should be aliquoted into small portions and stored at −70 °C
  before extraction because fragmentation of CFDNA might be caused by
  repeated freeze–thaw cycles
  
  For the THP method, 500 μl of plasma/serum was mixed with 5 μl Triton X-100
  (Sigma-Aldrich, UK) and heat denatured at 98 °C for 5 min. Samples were placed on ice
  for 5 min, then extracted with an equal volume of phenol–chloroform–isoamyl alcohol
  (25:24:1, v:v:v) (Sigma-Aldrich, UK) and centrifuged for 10 min at 14,000 g. The
  aqueous phase was precipitated overnight with 1/10 volume of 3 M NaOAc and 2.5
  volume of 100% ethanol at −20 °C. The DNA pellet was washed with ethanol, air-dried
  and resuspended in 50 μl of ddH2O.
  
  In the THP protocol, 98 °C incubation was used to inactivate
  PCR inhibitors and denature proteins in plasma/serum samples.
  Different times and temperatures were tested before choosing this.
  Since we had noticed substantial DNA contamination in SDS, Triton
  X-100 was used in the protein solubilization step. Direct conventional
  PCR was performed successfully on heat-denatured samples
  and able to detect 25 ng/ml DNA, indicating that this simple
  procedure offered sufficient protein digestion and inhibitor elimination
  for PCR analysis. The THP protocol gave a significantly
  higher yield of pure DNA solution for qPCR analysis than the
  QIAamp kit. The THP protocol showed high efficiency even with
  small DNA fragments as low as 100 bp. 


You might want to read this: 
Xue, Xiaoyan, et al. "Optimizing the yield and utility of circulating cell-free DNA from plasma and serum." Clinica Chimica Acta 404.2 (2009): 100-104.

A quick search of google scholar also revealed a few other papers you might be interested in:

Fleischhacker, Michael, et al. "Methods for isolation of cell-free plasma DNA strongly affect DNA yield." Clinica Chimica Acta 412.23 (2011): 2085-2088.

UPDATE:

After reading this (Fong, Siew Lee, et al. "Comparison of 7 methods for extracting cell-free DNA from serum samples of colorectal cancer patients." Clinical chemistry 55.3 (2009): 587-589.) which gives about 7 protocols (sadly without any references for some reason) I went hunting for  came up with this:


  DNA was extracted from 1.0 ml plasma by phenol-chloroform method with slight modifications.
  One ml of plasma was treated with 1x SDS/Proteinase K solution (0.5 mg/ml) (1:1), incubated
  overnight at 56 °C followed by phenol-chloroform (4:1) treatment and centrifuged at 7 000 rpm.
  The upper layer was transferred into fresh 15 ml centrifuge tubes and the same step was repeated
  again; DNA was precipitated by adding glycogen (0.1 µg/µl), ammonium acetate (7.5 M) and
  absolute alcohol. DNA pellet was obtained by centrifuging at 7 000 rpm; was washed with 70%
  alcohol at 10 000 rpm, dried and finally dissolved in TE buffer at 56 °C and stored at -20 °C until
  further use.


You can read about the above method here: Singh, Deepika Misra1 Renu, and Monisha Banerjee. "A simple and reliable method of obtaining fetal DNA from maternal circulation; its accuracy and sensitivity."

Also, if its available to you, it might be worth it:

Gahan, Peter B., ed. Circulating Nucleic Acids in Early Diagnosis, Prognosis and Treatment Monitoring: An Introduction. Vol. 5. Springer, 2014.