Can I transfer a Windows 10 licence to my new PC if it was upgraded from a retail licence?

Assuming my Windows 8 license is a retail license this would surely allow me to transfer it between machines?

Yes; Here is the EULA for Windows 8 Professional and Windows 8.

Can I transfer the software to another computer or user?

You may transfer the software to another computer that belongs to you. You may also transfer the software (together with the license) to a computer owned by someone else if a) you are the first licensed user of the software and b) the new user agrees to the terms of this agreement. To make that transfer, you must transfer the original media, the certificate of authenticity, the product key and the proof of purchase directly to that other person, without retaining any copies of the software. You may use the backup copy we allow you to make or the media that the software came on to transfer the software. Anytime you transfer the software to a new computer, you must remove the software from the prior computer. You may not transfer the software to share licenses between computers. You may transfer Get Genuine Windows software, Pro Pack or Media Center Pack software only together with the licensed computer.

Is it possible to clean install Windows 10 in this scenario

No; You don't have a Windows 10 product key. So it is not possible to perform a clean install, without first installing Windows 8.1, and upgrading that installation to Windows 10. You can of course choose not to keep anything or after you perform the upgrade once perform clean installations on the same hardware in the future.

Author's Note:

When I wrote this answer the above statement was true. As I later explain in new section about Threshold 2 is that it will be possible to activate and install Windows 8 with an eligible license key throughout the period the free upgrade is offered. How Windows 10 activates using this new method will remain unchanged.

Before Threshold 2 by accepting the Windows 10 free upgrade offer, Windows 1 used a digital entitlement system in order to activate. This meant that provided you performed the upgrade at least once before July 29th 2016 you would receive said entitlement to Windows 10. This also means you are eligible to upgrade as many machines as you want (within reason), use only one of those machines at a time, provided you do so before that date. This all is true but only for retail versions of Windows 10.

As I explain later with the release of Windows 10 Threshold 2 you will be able to activate Windows 10 and activate the installation of Windows 10 for free with an eligible license key provided it is before July 30th 2016. As I explained it as not been revealed what will happen if you attempt to activate Windows 10 on a machine with said license keys, that never attempted to activated Windows 10 before July 30th 2016.

Would this mean that it is possible install Windows 10 on my new machine and if so, how would I go about this?

You install and upgrade your Windows 8 license to Windows 10 using the appropriate upgrade path. See my previous explanations for more information.

Would this be a case of just doing a clean install (and if so, what product key would I enter) or would I need to install Windows 8, upgrade it to Windows 8.1 and then perform a second free upgrade?

See my answer to your previous question about how you would install Windows 10 on a new machine.

Can I use a Windows 7 or Windows 8.1 license to install Windows 10 Threshold 2?

I have added this section after reading information about the new activation functionality that will exist in Windows 10 Threshold 2. Once this update has been released this November ( November 2015 ) it will be possible to install and activate Windows 10 with the license keys of previous eligible versions of Windows. This means that a retail license of Windows 7, Windows 8, or Windows 8.1 can activate Windows 10 on multiple devices.

You are of course only limited to run a retail license of Windows on a single machine at a time. This also means that you would perform this type of upgrade before July 29th 2016 in order to upgrade to Windows 10 for free. It has not been revealed what would happen if you attempted to do this on July 30th 2016.

I have provided Microsoft's reasoning on this change below. I have eliminated the reference to Insider Preview to maintain the accuracy of this single edit in the future. The Insider Preview build they are speaking of is that for Threshold 2 not the rumored Windows 10 Redstone update which would precede this series of testing.

We have received a lot of feedback from Insiders on making it easier to activate Windows 10 on devices that take advantage of the free upgrade offer to genuine Windows by using existing Windows 7, Windows 8 or Windows 8.1 product keys. If you install this build (Threshold 2) of the Windows 10 on a PC and it doesn't automatically activate, you can enter the product key from Windows 7, Windows 8 or Windows 8.1 used to activate the prior Windows version on the same device to activate Windows 10 by going to Settings > Update & security > Activation and selecting Change Product Key. If you do a clean install of Windows 10 by booting off the media, you can also enter the product key from prior Windows versions on qualifying devices during setup.

Microsoft's Stance

Since the author edited the question after I submitted this answer and clarified their question only after the fact the proceeding information was not in my original submission.

I'm asking if I'm eligible for a second free upgrade from a retail license of a previous version of Windows regardless of the path I'd need to take to achieve it.

If you want the upgrade for free you would need to perform the second upgrade using the supported upgrade path before July 29th 2016. This is possible because your original Windows license rights allow you to format that original machine, install the retail license on your new machine, and initiate the upgrade. After the Threshold 2 update is released you can install Windows 10 directly on that new machine you can install and activate it with that eligible key. After July 29th 2016 even doing that will require you purchase a Windows 10 license.

To answer the question:

I'm asking if I'm eligible for a second free upgrade from a retail license of a previous version of Windows

Yes, you can upgrade a valid, activated retail license of Windows 7, 8, or 8.1 multiple times during the free upgrade offer period (i.e. until 29th July 2016).

BUT: This does not upgrade you to a retail copy of Windows 10

Even if you upgraded from a retail copy of a previous version of Windows, you do not get a Retail license for Windows 10 through the free upgrade offer. A Windows 10 license obtained via a free upgrade is tied to the hardware you upgraded on and cannot be transferred to another PC. You can however relinquish your Windows 10 license entirely by downgrading back to your previous version of Windows, and reactivating your Windows 7/8/8.1 retail license, which can then be itself transferred according to your license terms.

So what does this actually mean for me?

You can downgrade back to Windows 7/8/8.1 retail, transfer that license, and upgrade again for free, as long as you do it during the free upgrade offer period. Remember the free license is not transferable, so after the end of the offer period you can still downgrade to your previous version of Windows but cannot upgrade again without paying for a retail license.

Some people have had success obtaining a transferable retail copy of Windows 10 via Microsoft's support escalations department:

http://www.tenforums.com/general-discussion/14021-windows-retail-version-upgrading-win-10-oem.html#post325037