I may be offered a job in Norway at the end of the year and, as such, have been looking at visa options. I will be getting a Norwegian work permit once there but I am also eligible for the UK Ancestry visa which is valid for 5 years and enables the holder to work freely and eventually obtain UK citizenship. Is it possible to have both? I am in the Oil and Gas field so there will also be job opportunities available in the UK sector of the North Sea field no doubt. It would be nice to switch between the 2 zones easily if need be.

As far as the UK is concerned, there is no reason why an individual cannot apply for, and recieve, as many different visas from as many different countries as one is eligible for at the same time. I assume that Norway is the same.

However, remember that to obtain a UK ancestry visa you will need to demonstrate that you intend to work or seek work in the UK. Also to qualify for permamnet residence in five years you will need to have spent the majority of that time living and working in the UK. See Guidance - UK Ancestry (INF 9)

I can't see much advantage to you activating your UK ancestry entitlement while you have a work permit for Norway, in fact it might work to your disadvantage in the long run. This is what the Entry Clearance Guidance says about offshore oil workers:

"Chapter 18.8 Offshore workers

UK immigration legislation does not extend to installations operating wholly at sea on the UK Continental Shelf. Therefore, there is no prohibition on overseas nationals taking employment on offshore installations. However, because offshore workers usually work on a rota basis, spending so many weeks working then an equal number of weeks shore leave, they normally tend to base themselves and any dependants in the UK, so although they do not require a work permit for off-shore employment they and any dependants do require leave to enter or remain.

Entry clearance

Subject to normal visa requirements, off-shore workers are allowed to live in the UK during their shore leave exceptionally outside the Rules and their dependants are also exceptionally allowed to base themselves in the UK.

Entry clearance is not mandatory for non-visa nationals except if you are a national of one of 10 non-visa countries and intend to stay in the UK for more than six months. A work permit will only be required if any part of the work is on-shore.

Entry clearance endorsement

For only off-shore employment entry clearance should normally be given for 12 months Code 2"

So, you don't need a work permit to work outside the 12-mile limit, and unless you're coming ashore for more than 6 months at a time, you could enter as a visitor.

I suppose you could enter with the UK Ancestry visa and argue that your base is the UK, and it's immaterial whether you're working in the Norwegian or the UK sector. However, when you come to apply for settlement in the UK after 5 years they would probably discount the period for which you had a Norwegian permit.