I work in O&G. I’m sure it’s not unique to this industry but they will be swamped (1000s) by “adequate” CVs. i.e. Expected 1st, 2:1 from good uni, some experience. The adequate ones get put through to interview where they are weeded out. No one reads them in massive detail. They’ll probably let 10-20% through, maybe with a telephone interview to cut it down further.
1. Get help with your CV. Get someone who’s opinion you value to read it over. Use uni careers service if they can help. At least then you’ll know your CV is presented as well as it possibly can be.
2. Emphasise any experience you have that other might not. Have you set up / run a club at uni or out of uni? Have you been doing part time jobs?
3. Tweak the letter / CV for each company you apply. Get hints on how to tweak it by reading corporate guff on their website.
If you’re struggling in your chosen field (which is a narrow /specialist one) why not apply to other companies? A placement with any reputablle engineering company would help you massively, even if it’s in a different field.
edit: I know IChemE publish a list of 100s of graduate employers, check if the IMechE does similar. Might give you a wider list of people to apply,