Dan I have just completed a couple of split years between the US and UK and completed UK and US taxes largely myself. You can PM me if needed.
The US federal side of this is actually easier than the UK since the US taxes your worldwide income regardless of where you are living and working, and then you claim a foreign tax credit for taxes paid to foreign governments. So you just file with your US and UK income combined, converted to dollars, and use form 1116 to claim a foreign tax credit for any UK income taxes paid (but not national insurance). The US state part is the one to be wary of because you might meet full year residency and be double taxed by your state on your UK income - fortunately state income taxes are usually low - California being the notable exception.
It's the UK part that I think will be more complex because if you're continuously going back and forth you won't be able to claim split year treatment. I think you'll need a competent UK tax adviser for this. Mine was easy because I was in the UK continuously for about 14 months so I could file two split year tax returns. If you're going back and forth over multiple years I don't think they allow this and it seemed to me to get quite complicated with counting how many days in the UK etc etc.
The other thing to consider is healthcare. I suspect you'll end up paying US health insurance all year because you may not qualify for the NHS (or at the least there may be gaps in coverage) and you can avoid the ACA penalties. I didn't look into worldwide health insurance so can't help there. We went straight from US insurance to the NHS and back to US insurance but again I'm not sure you can reliably do this if going back and forth. Getting US insurance on can also be complicated because many insurers will not sell a policy without a US address, but of course you can't arrive in the US and get an address without having health insurance (or risk bankruptcy if you get sick/injured shortly after arriving). A friendly insurance agent gave me some tips to get around this - in the end my US employer put me on their insurance before we arrived back in the US.
You could ask your prospective employers to see if they can cover the cost of having a tax accountant do your UK return since I think it will be complex (and expensive).