(having been thinking about my reply to this since you posted, but can't remember password to log into MN on phone so have had to wait until the weekend when laptop is on...)
I was lucky enough to be one of the primary maths specialists the DfE took to Shanghai last November, and we had 2 teachers from Shanghai teaching in my school in January. That came about because a couple of years ago I was lucky enough to be selected by NCETM to be trained as a primary maths mastery specialist, to implement the best of what was seen on the first primary Shanghai exchange two years ago. Having completely changed my approach to Maths teaching and supported my colleagues in my school to change, I'm now working with a number of local schools, supporting them to implement teaching for mastery.
Singapore/Shanghai Maths and Maths mastery as some of the most misunderstood concepts in teaching at the moment, in my experience because they all mean different things to different people. It just isn't possible to take a system of teaching from any other country and transplant it here. Our culture is different, our children are different, our parents are different, expectations are different... But what you can do is pick the best of what they do and match it with the best of what we do (because they are very aware that they have a lot to learn from us too).
For me, Singapore/Shanghai/mastery maths is about teaching for deep understanding. Slowing the curriculum down. Spending longer on each topic so that children really understand what they are doing, rather than the superficial, one dimensional learning that the spiral curriculum often produced. Giving children the chance to transfer their new knowledge from their finite, short term memory to their infinite long term memory so that you don't have to keep revisiting topics because they've forgotten most of what you did when you last covered the topic. Giving them the skills to use their knowledge flexibly. Teaching them to reason and to communicate their reasoning. Enabling them to apply their knowledge in a range of different situations. I don't think any teacher would argue with any of that. What is up for debate is how you achieve these aims.
Inspire Maths/Shanghai Maths/Maths No Problem/whatever are just resources produced by publishers to help schools teach for deep understanding. They all have a slightly different approach and organise things slightly differently. So it's impossible to say what a school means when they say they do Shanghai Maths.
The journey through the lesson, with small, clear steps from the initial starting point to new knowledge is key, as is thinking carefully about the examples a child will work through. Yes, there is repetition but it certainly isn't mindless repetition because of the conceptual/procedural variation in the examples they will experience which are designed to deepen their understanding as they work through them.
#Maidupmum - in terms of doing research before an interview lesson, I'd have a good dig around on the NCETM website as they have lots of good resources to support with teaching for mastery. I'm pretty sure a 5 part lesson is part of Inspire Maths (OUP) so a google for that might dig up some useful reading. I've told my colleagues that the three part lesson is dead, but you can now have as many parts to the lesson as you feel is appropriate for your children. You might have a 1 part lesson today and then an 8 part lesson tomorrow. It's about good teaching - knowing your class and tailoring your teaching to match their needs. I'm more than happy for you to pm me, or to try and answer any questions you have. Good luck!