I am an engineer with about 15years experience in the Oil & Gas space. I have worked projects and in asset management across 4 continents and steadily risen through the ranks.
Right now, I'm technical advisor to the CEO of an NOC affiliate.
I'm at the point where an MBA has become indispensable but I don't have the time to study for GMAT. My schedule is really hectic and adding studying for GMAT to my plate now is not possible.
Are there any UK-based full-time MBA for 12-18 months that I can apply for without the bother of a GMAT result.

This really depends on the quality of the MBA you want. My guess is, if you are working with NOC affiliates, that few people there will have excellent MBAs from schools which require the GMAT. If you want to stay at that level, really any accredited UK MBA will do. I suggest http://www.rgu.ac.uk/business-management-and-accounting/study-options/mba-degrees/master-of-business-administration/

However, considering the year you are investing it doesn't really make sense to not take the GMAT, even if you only take the test without preparation and get a weak score. Schools that require the GMAT won't expect you to get the same score as a 24 year old.

Take a look at Why you should take the GMAT http://bit.ly/WhyGMAT

The GMAT schools are so very much better. Imperial College, for example, would give you a world class education. Warwick has a specialised energy MBA.

Please take the GMAT, the GRE is milder in the Quant section but the Verbal is killing if you are non-native speakers in the sense that they put unnecessary emphasis on knowing colloquially long and ambiguous words that you never come across again in your life.

Both are equally useful in your situation.

Yes, indeed: if you're willing to put your career on hold for 12 or 18 months it's really not that much of an issue to take the GMAT. It's a much, much smaller investment compared to the entire MBA, and will pay off by allowing you to apply to better schools.