Honest answer, no Portsmouth doesn't particularly have a strong or established reputation with the oil industry. Graduates from their are bound to face tough competition from established institutes, Imperial, Heriot Watt, Manchester.
However this does not mean Portsmouth graduates have no chance. My advice if you're studying at Portsmouth is to try very hard to get an internship with one of the major oil companies. An internship is an easier way to a permanent position than direct graduate applications. The other thing to consider is doing the Pet. Eng. MSc at Imperial or Heriot Watt afterwards to compensate for institutional reputation.