We have done this twice.
You can both be on SPL at the same time but obviously that means you have less time in total - you have 52 weeks and the mother must take the first two weeks. So if you are off for four weeks together, that means one or both of you will be at home for 48 weeks in total - does that make sense?
His two weeks of paternity leave is calculated separately from SPL.
My understanding is that SPL can be taken in more than one block but it must all be consecutive (eg within the 52 week period) and in blocks of at least 2 weeks.
With DC1 we did what you plan to do: I took the first nine months and DH took the last three. Overall, this worked quite well. In hindsight, I would rather have had a bit longer and he would have been happier with less.
Despite having been very involved with DC1, DH found it a HUGE shock to the system to be flying solo for three months and also found it very isolating. Despite being in a very progressive part of London, he was generally the only dad at groups and so on, which made him feel uncomfortable so tended to stick to parks and soft play. But overall we’re glad we did it as it set a good precedent for equal parenting.
Second time round (2020, this is relevant), we decided DH would take four weeks of SPL in the summer to coincide with DC1’s school holidays, when DC2 would be around 7 months. In hindsight, we should have cancelled this as Covid and lockdowns meant we were all sick of the sight of each other and DH had enough annual leave to have covered a fair whack of the summer holidays anyway.
I would probably recommend you have an overlap followed by some time for DH/DP to fly solo. But you are right to say you would have annual leave to use up after SPL so could be on annual leave concurrently with DH being on SPL before you return to work.
Also bear in mind that you can sometimes split the pay as well as the leave - in our case, we chose for me to take the unpaid stretch of the year and DH to take the paid entitlement as he earned more. This was how it worked with our employer.
What made the biggest difference for us with DC2 was having DH work from home from around 8 weeks. For building a strong relationship this was “better” than SPL. If we were having a third, I’d do everything I could to make sure DH was a part of DC3’s daily life, every day (which didn’t happen with DC1).