OP - none of this is at all your fault but please be careful about what you say in your next interview. I know you don't plan to "slate" them but I think you are comfortable with a degree of openness that won't reflect well on you at interview - when they don't know you yet.
"No progression opportunity in the role after the description was changed"
Be careful how you say this one. Saying "I thought there was more opportunity for progression than turned out to be the case" sounds fine, but saying "they moved the goalposts" sounds a bit like you're whining about them as an organisation. It might also sound like there might have been opportunities, but you weren't being offered them as you hadn't convinced them by your performance. It's tricky to get the tone right so be careful you don't sound like one of those "everyone is against me and it's always someone else's fault" people.
Can I just say that being discreet and positive is always looked upon well. They might suspect the truth - your previous employer was a shower - and respect you for not bluntly saying so.
"2. Company is in financial difficulty "
A tricky one. Might sound indiscreet; might sound like you weren't succeeding and blaming everyone else.
"3. Existing internal relationships made it impossible to do my role (the agency issue - I found out late yesterday that their is a silent partner investing in both businesses - hence they will never end this relationship despite, in my opinion, the agencies incompetence)."
Again, this is the basic truth - you were misled about the job and set up to fail - but don't say it! This sounds indignant, critical, and a bit self righteous.
I interview and for me is a real red flag when people come into interviews full of criticisms of others. Even when I know that the person is leaving because their boss is a twat (because I have personal knowledge of that boss and know they're a twat) I respect them far more when they don't come in all full of indignation and bitterness about being expected to work for a fool and no one recognising their genius. At work, when people share out credit for successes and take responsbility for fuck-ups, they all go up in my estimation.
This is a real learning experience for you. It's horrible but look at it in terms of how you can evolve as a person. It was a massive step change in my career development when I stopped thinking about justice and righting wrongs against me and making sure people knew I was right; and started thinking about to get out unscathed and manage nasty people without getting drawn into their swirl of acrimony.
I would say something like: "The relationship with the agency was deeper and more long term than I realised, so it was less of a hands on role and more about managing the agency - which is a great job, but not where I want to take my career right now, so I am looking for a job that can take me more back into doing x,y,z directly rather than managing an external team"
(Obviously if that makes sense for your line of work and what you want to be doing!)