It has recently been announced that the A'Mhoine peninsula in Sutherland, Scotland will be host to the United Kingdom's first vertical launch site (assuming they can get anything done with just £30m in grants). Lockheed Martin, Rocket Lab and Orbex have been put forward as launch providers.
It is suggested that the launch site will allow for polar and sun-synchronous orbits, primarily for small satellites:
Launch vehicles taking off from Scotland’s coast in Sutherland will fly to the north, taking routes over the Norwegian Sea between Iceland and Svalbard to ensure debris does not fall on populated areas.
Is there an official word on the range of orbital inclinations to be targeted from A'Mhoine?
And what is the range of launch azimuths available? How much will these be affected by the (sparsely) populated Orkney and Shetland islands?
A'Mhoine is at a latitude of ~58.5° so this is our minimum possible inclination without plane changes.
For prograde launches, by my rough eyeballing, a very significant dogleg could reach a ~50° inclination, but any less than that would cross over western Norway.
Northerly launches to polar orbits have a fairly wide range, but will be limited by the large number of inhabited islands.
Retrograde inclinations greater than ~98° for typical sun-synchronous orbits are of limited use, but a wide range of Westerly launches over the North Atlantic would be possible (up to a launch azimuth of ~170°).
Scott Manley posted a video discussing the A'Mhoine launch site with targets of sun-synchronous and polar orbits. It featured the linked graphic with viable launch azimuths that avoid the Northern Isles. It appears to be hand-drawn though (no, really!) and doesn't reference any official information.
Gov.uk has a large collection of documents from the many consultations on the prospect of a UK spaceport. As expected however, most of the analysis is concerned with the politics and finance and there appears to be very little detail on the physical feasibility of a launch site.
The closest they seem to come to describing planned launch azimuths is:
...it is important to be clear that, due to its northerly latitude, the UK is only suitable for launching satellites into polar orbit (as opposed to equatorial orbit).
The UK Space Agency's prospectus also briefly mentions sun-synchronous orbits (which are close to Polar orbits anyway):
Launching rockets north from the UK allows access to in-demand polar and Sun synchronous orbits.
Related question about launches from Europe as a whole:
This has more detail on the proposed launch providers: